Yeah this thread has gotten out of control but let me quickly bring you up to speed the best I can by answering all of your questions.
"When the engine dies"
1.) The engine doesn't even make it to idle. It starts and dies please see
adding choke just does the same thing at a higher RPM.
2.) If I rev the engine it dies in the same amount of time as in the video.
"Immediately after it cuts out and won't restart, have you checked to see that...."
1.) It will restart immediately after dying on me and I have a spark tester and I see a nice light every fire
2.) I am not sure about fuel on the spark plugs I didn't pull them out between fires but the bowls are full and as I said before it will fire/die again right after.
good video and some very helpful information .
So we've learnt some important points . It starts willingly and runs without backfiring or popping so its highly likely that the timing isn't far off.
The wiring loom is just hanging loose which could mean that you have poor or inadequate grounding somewhere or possibly a short. Check that all the electrical componants that need to be bolted to the frame for a ground are grounded somehow.
The other thing I would suggest is to disconnect the gas tank from the carbs and rig up a plastic bottle to feed the fuel line to the carbs and use some fresh gas.