Just to clarify what I wrote about the headlamp switch, it should have a 'C' for charge position, so charging (if any) can be switched on or off.
Re the centre stand, these were notorious for rotting away. You will find that a C10 centre stand (29-4860) will fit, but you will have to drill the stand legs and fit 2 short pegs to act as stops. They often turn up on ebay, and are also available from dealers, but quite expensive.

A few random thoughts, which may or may not be helpful. It all depends on what you want to do with the B2.
I imagine the gearbox had split because the kickstart stop had become loose a few times over the last 90 years, and the motorcycle had probably fallen over onto the kickstart a few times. The stop does tend to come loose, so keep an eye on it. You should fit a rubber sleeve over it with a steel outer (like a silent bloc bush) otherwise the rubber will only last a few weeks.
I know it's too late now, but mainshaft and layshaft endfloat are critical for a good gearchange. If you ever dismantle the gearbox again, you might want to fit a sealed bearing to reduce oil leaks. One of the problems is that the layshaft is often slightly bent, which makes setting endfloat nearly impossible.
Your kickstart ratchet pinion is very badly worn. I've not seen a worse one, and you may find  that it either slips or jams in use, although the quadrant looks to be in quite good condition. I would try to find a new one as a matter of urgency.
Cam wear on B2's seem to be quite high, so it might be worth checking how far the valves open. I eventually found mine were only opening 1/8".
If you split the flywheels, note there are a pair of con rod thrust washers on the flywheels with chamfers on them. They can be drifted out through holes on the outer faces of the flywheels. They must be fitted with the chamfers in a certain position. The chamfers allow more oil into the big end. Oiling is splash only. There is no feed to the big end. It would be very worthwhile getting hold of a copy of Bruce Main Smiths green book of BSA's 1935 to 1940, in which he shows the position of the chamfers, and many other things.
You will probably find the unbushed little end is badly worn. Alpha Bearings can bore out the eye and fit a thin wall bush if required.
Your petrol tank with the raised ovals, is from a later machine. Yours would have had threaded oil and petrol filler holes and alloy caps. But as long as it doesn't leak.............
The original advance/retard would have been a twistgrip on the left handlebar. The bar would have been slotted to accommodate it.
Replica twist grips are available from Cornucopia in Germany, but they are made up of a lot of parts and are quite expensive. So you may want to fit a lever control for the time being. There would also have been a valve lifter fitted as part of the original clutch lever. These levers turn up on ebay every now and then, but again, they are prohibitively expensive.
I think your backstays may be from a Blue Star Junior, but as long as it all lines up...........
Carburettor settings, Main jet 75, needle jet .106, slide 4/4, needle position 2.
I set my pilgrim pump to 1 drop every 3 or 4 seconds.
Terry's valve springs are part no. VS 22.
The Maglita is a very wonderful instrument. Set points between 0.010" and 0.012" and see which is best for starting. If you're lucky it should produce about 2 Amps unregulated. Your headlamp switch should have an "off" position as a 2A charge on a long run may strain an AGM battery. They don't like it up 'em.
I set my maximum ignition advance to 35 degrees BTDC which seems to give good results. Spark plug gap 0.018" or 0.015 if it gives better starting. I highly recommend checking your valve timing figures against BSA's figures. After all, every little helps.
Finally, I believe the engine would have been designed by a fellow called Harold Briggs, who was BSA's Chief Designer in the '30's  before Val Page took over.
Let us know how you get on.

Sounds a bit like the engine is "hunting", but this normally occurs at a smaller throttle opening and indicates a rich mixture. If you have no success with the carburettor, I wonder if the cush drive might need tightening a little?

The spark should jump a 5/16" gap. Assuming the points are clean and set to 0.012", I would have a look at the Brightspark website for inspiration.
In my experience, the armature will require a rewind and new condenser, but you may be lucky. I would recommend APL for rewind if required.

Bob,
If you do a search on the internet for Bushman's Carb Tuning Secrets, you may find it quite interesting.
My own thoughts are that you still have a blockage in the pilot passageways.
Unfortunately, the only way to verify this is to remove the alloy blanking plug opposite the pilot air screw. You will probably destroy it getting it out. I don't know if new ones are available. You will then be able to see that your nozzle cleaner is going all the way through the jet. At the moment, I don't think it is. Maybe you could try an ultrasonic cleaner?
I think I would drip or preferably spray a little petrol into the intake, while trying to start it, or perhaps a little petrol through the spark plug hole. It should then at least start.
If you still think it's an ignition problem, you could invest in a Spark Gap tester. This will tell you if it's sparking under compression.
Good luck, and keep at it. You will get there in the end.

Thanks for the feedback. Glad to help. Let us know if you ever manage to cure the click.

The red D.W Munro BSA book mentions tappet click on a couple of occasions.
Firstly, he suggests it can be caused by excessive cam endfloat, which should be no more than 0.002". Unfortunately, this can only be checked when the crankcases are split.
Secondly, he suggests it can be caused by incorrect meshing of the pinion teeth, for which the cure is either fitting new standard size pinions or new slightly oversize pinions, which he says are available. I've never heard of them, so perhaps they were only available to the Factory?
To diagnose the problem, if you look very closely at the teeth when turning the engine very slowly, just as the cam starts to close the valve, you may find wear on the teeth allow the cam to rock over as the play is taken up, causing the click......if you see what I mean?
Anyhow, if you insert a thin piece of shim, or cardboard or even rag into the offending teeth, and gently rock the engine back and forth, and the click disappears, you will have diagnosed the problem. I have yet to find a solution to it, but you might try a new half time pinion and cam pinion.
Hope this helps.

Jean Luc's post has reminded me that I haven't posted an update.
I took BRM's advice and removed the valve. I made up a regulator and pressure gauge, and found the valve wasn't sealing at all.
The lead seal wasn't marked with 5 or 10, but it did have the Piled Arms stamp with the letter B (1934). Great shame, but I had to melt it to gain access.
I removed the screw, spring and ball, which was a bit rusty. I renewed the ball, but it still wouldn't hold any pressure. I could see that the area around the seating was raised up, so I tried to ease it down as best I could, but it wasn't very successful. Maybe you could you a small end mill bit?
So, although the valve body is steel, all I could do was tap the ball into the seating. It took about 3 or 4 tries, but eventually it sealed. I adjusted it to 7lbs and soldered the end up.
When I started the bike, I had no oil pressure, so I removed the brass adjuster toggle and unscrewed the oil regulator screw, and the oil pressure increased, so I set it to about 8lbs at half a turn out.
I now have a steadyish oil pressure of about 7 to 8lbs, hot or cold and on tickover (which seems a little odd, but I'm not complaining).
So thank you BRM. I would never have got there by myself.

Neil, Is Choke on a typo? Mine are all pull wire tight choke off.
DGB, If you are new to all this, you are on a steep learning curve, but it will get better with practice.
It's not uncommon for these old bikes to be difficult to start, and a lot of it is down to starting technique.
Follow Neil's advice, and if it doesn't start, then perhaps alter the advance, or throttle opening, maybe try it with a closed throttle? Try it with either less tickling or more tickling.
An easy way to check if fuel is getting through is to examine the spark plug. Is it wet or dry? If it's wet, maybe you are tickling it too much or using too much choke. If it's dry, maybe more tickling or choke and try to start it with the throttle closed, to draw more mixture in. Hopefully, you will discover the technique your bike needs to start it.
Otherwise, it's diagnostics. Pilot jet blocked? Magneto breakdown etc. A simple test would be to invest in a neon spark plug tester. It's not a full test, but it will tell you if there is no spark.
Let us know how you get on.

Well, this is all getting a bit complicated, But I think I've finally worked it out.
Firstly, I have Joseph's footrests in front of me. They look identical to the ones British Austria are selling.
The right hand footrest 15-8167 (with the boss) is correct.
The left hand footrest he and Joseph are selling (15-8156) is not for a Blue Star, but fits other models. So they are not a pair.
The footrest you need is 15-8158, but I have never seen one for sale.
However, if you look in the Parts Book, they both look very similar, with the angle of the bend being different. I doubt this matters much.
But, as I mentioned in my previous post, when fitted, one is 1/4" lower than the other. I think you should be able to enlarge the slot in the footrest to get them to line up.
You will also need 15-8161 which is a simple thick tapered plate and fits between the frame and right hand footrest.
Finally, you need 15-5748 which is a slightly complex distance sleeve, which fits between the frame and the left hand footrest.
Confusingly, this is shown in the Frame and Fittings section of the Parts Book, but you should be able to work out what it looks like. I got mine from Joseph.
Hope this helps.

Jean-Luc,
Good to see you have the later enclosed clutch basket. This should help.
Let us know what your oil pressure is / was.

From what you say, it sounds like you are over oiling the engine. I would start by removing the brass adjuster knob on the timing cover, and screw in the splined adjuster, counting the number of turns until it bottoms. BSA recommended from half to one complete turn out. If it was set at more than this, you are probably over oiling your engine. Hopefully this will give you around 8 lbs/sq.in. on your gauge and a puff of blue smoke from the exhaust when opening the throttle after going down a short hill with the throttle closed......assuming your rings are in good condition. If there is no smoke, you are probably under oiling.
It might be an idea to empty the chaincase trough by stuffing a rag in there to soak up the oil, and drain the crankcase. This will allow you to start from scratch.
I think your adjustment of the oiler is OK, but I wouldn't turn it down any further.
You'll probably find that the friction ring behind the chainwheel is covered in oil. I've never had any luck cleaning oil off the rings, so replacement may be the only answer, but only after you have sorted out the oiling.
Incidentally, later Blue Stars had a chainwheel which enclosed the clutch with a steel ring, presumably to prevent oil getting into the clutch, but this won't stop oil getting onto the inner disc.
Let us know how you get on.

Simon,
Don't forget the B2 has a total loss oiling system. If oil does not drip after a run, there is something wrong. I would expect one or two teaspoons of oil under the engine after leaving the motorcycle for about an hour. If it's a lot more than that, you might want to check how many drops of oil your Pilgrim pump is set at. BSA recommended 14 to 16 drops per minute, I assume at normal running speed. I set mine to 1 drop every 4 seconds at tickover speed.
However, I think the most important thing is to ensure there is a hint of blue smoke from the exhaust when opening the throttle after going down a short hill with the throttle closed (assuming the piston rings are in good order). This indicates to me that engine lubrication is about right.
If you still have a problem BSA Service Sheet No.48 (in the Club Library) mentions a restrictor bush fitted to the chain oiler stud, although you don't have a trough in your chaincase. The Bruce Main Smith green book of BSA's 1935 to 1940 also mentions this as having an ID of 0.46".

I imagine it's the same as the 250 Blue Star. This has various drillings in the crankcase wall, which connect with the end of the threads for the lower chaincase mounting stud. The stud is part hollow and drilled at a right angle to allow oil to drip onto the chain. There is either a knurled adjuster, or an adjuster with a locknut located vertically behind the cylinder on the left hand side.
As an aside, it always sems to me that since this is the engine breather, the drillings are quite small, and BSA recommended turning the adjuster down to prevent oil entering the clutch, this would result in excessive crankcase pressure. The only saving grace would be the pressure being released into the integral sump.
Anyone got any thoughts on this?

From what you have said, I'm sure we are talking about a pre-monobloc carburettor, even tough you have entitled it Monobloc.
It's interesting that you have had a situation where it doesn't flood, indicating that there is not some manufacturing fault.
As Spaceman suggests, you should see what happens with the float chamber top removed. Is the needle bent at all?
It maybe worth using a little Brasso on the seating, just to polish it, in case there any high spots. You should then be able to see where it's seating or not.
I wonder if the needle is sticking in the float chamber top. Maybe apply a little light oil, although it won't stay there long.
I assume that if you pull the needle upwards with the top removed, it stops flooding?
It doesn't take much to prevent the needle from seating, so it may be worth filling an in line filter.
Let us know what you find.