..........Ok, but you did not answer my question fully. WHAT exactly are you running for an ignition system?
Here's the deal. ALL switched voltage comes from the ignition switch, of course. No mystery The outputs from the ignition switch are:
1...ACCESSORY, hot either with key in "accessory" or "run" this feeds to the "ACC" buss in the fuse panel
2...IGN1... "ignition run", dark blue--this is HOT ONLY IN RUN!! It is NOT powered in "start"!!! This feed things like oil light, cluster gauges power, and THROUGH THE bulkhead for underhood loads, depending on year, the VR, the alternator field, some smog doo-dads, electric choke if used, AND THE COIL BALLAST
3...IGN2..."bypass" normally brown. This only goes one place--to the coil + side of the ballast resistor. THIS IS THE ONLY source of power to the ignition system during "crank" It is hot in "start" but it is a DIFFERENT switch contact, so the two circuits are isolated
4..."start"...The yellow start wire....hot only in start, it only goes one place (except 74, seat belt interlock)...goes through the bulkhead connector to the start relay
So, HERE IS THE deal. If you still have the ballast hooked up as OEM, then during start, "battery" goes to the COIL side of the ballast, FEEDS BACKWARDS to the "ignition switch" side, and feeds back to whatever is connected to the dark blue IGN1 line
THIS MEANS that if you have it wired thus, there is VERY LITTLE voltage going to the EFI during "crank." FURTHER.........
If you have an ignition system that does NOT have a ballast, and if you do NOT have the OEM ballast connections connected together, then there is NO voltage to ANY of the ignition / EFI stuff during crank, and the only reason it fires and runs is that you "accidently" released the key partly or fully back to "run" and it re--connected the "run" line to power.
The other possibility is that you have a bad connection in a connector or the ignition switch........the switch connector, or the bulkhead connector.
I would "get on" the splice where you have the EFI connected, and clip a lamp or meter to that point so you can monitor it a few times while cycling from start to run with the key