Not quite with you.
You have a Mk 12 type E Invacar, that would normally have a reversing dynostarter driving a Villiers 11E. So all sounds normal there.
To start in forwards you turn the ignition key so the ignition light comes on, the reversing light does not. If the neutral light is working, it should be in neutral. Turn the starter on, feed in some choke and it should catch. Off with the starter and let it warm a little and let the choke off. This should happen in a matter of 5 seconds or so. You can catch the engine on the throttle, it probably will not tick over for a minute or so, but to much choke can prove to supply to much fuel for the plug to cope with, and it will stall from a wet plug. When starting therefore it will initially be smokey. As you feed the choke off it will clear, but remain visible until the engine is warmed up. When running, tuned correctly and hot, there should be only a hint of smoke at the very end of the exhaust. Clearly it should tick over at a nice lobbing rate.
The dynostart just offers starting. While the ignition circuit passes through it for switching the points to reverse, it clearly is working, at least forward, in your case as the engine runs. The unit starts turning when you want it, stops when you want it. So that works. So there cannot be a lot wrong. You can try reverse, its always less keen to start in reverse as your running on the charging coils, smaller than the starting coils. If it does turn in reverse and the points are set, it should run, and that confirms all is pretty much well.
Stalling might be not enough choke. Might be poor tuning, or a slack throttle cable. Might be to much choke, a fuel leak filling the engine with excess fuel while stood idle, are just poor tuning. If there is a lot of smoke and it takes some time to diminish, then clears to near nothing, it is more like a fuel leak/tap issue. If it remains a smoky car then the tuning is out.
If starting with a flooded engine, no choke, throttle wide open and a fair length of churning my be needed before the unit will cough, and stutter into running on the throttle. It will then need to clear itself and will smoke like a bonefire for a bit.
Once running check that the ignition light is going out when the revs rise. A permanent light means there is a problem, could be simple, could be nasty. It is not unusual for the light to flicker, or glow occasionally. This is either some poor wiring in the unit, or a dodgy regulator. Normally knocking the reg when it is glowing will tell you which, as if it is the reg, the light will often go out as the reg resets itself after the knock. If it is not contiguous with beating the reg, then a dynostart service is well due. Clearly a dynostart leaking charge anywhere needs resolving. It can only get worse. It drains power from the ability to start commensurate with the seriousness of the short.
I am no expert at tuning either Villiers, or the Villers carb. I cannot imagine its any more difficult than a Sachs, but I leave you with the Villiers experts for that.
