If the fuel and spark occur at the right time ( in regards to tdc ) it will run. But mine kinda tries to for maybe 5 or 6 attempts and then seems to flood.
The pictures show the item we think may be the case but they are hard to source and expensive ( €350 ) to throw in as a maybe. Damn these old cars

Last pic is what AI gives as its description
It's not a part I am familiar with, if you are sure it only times the injector pulse and not the ignition, I don't think it is your problem.
However I maintain that regardless of fuel going in at the right time or not on a petrol engine, as long as the spark is timed correctly, you could physically tip petrol down the inlet and the engine would run, obviously if you tip too much petrol in it would flood .
I have even seen a car that has run out of fuel and to prime the manual fuel pump to draw in new petrol a car was started using hair spray squirted down the inlet with the air cleaner cover off!!!
I am not saying the engine would run perfectly, but as long as measured amount of petrol, as in not enough to flood engine or starve it, then engine would run.
Pull the fuel pump relay out and carefully put a drop of fuel down the intake, the engine will run until it uses that bit of petrol up.
Only use a small amount of petrol, don't spill any and probably a good idea to have a fire extinguisher handy.
Don't try to rev, just keep a small throttle opening, the only danger is if you try and rev the engine and it backfires whilst you are tipping in petrol, so not a good idea.

Having said that I have seen carbs in the old days with flames, but if foot taken off accelerator pedal and engine still cranking what it does is suck the flames down the inlet and it goes out with no ill effects. Fun to watch though.
