Strange starting issue

There is no such switched circuit, that's why I made the suggestions. The switch on those cars has:

Battery in to the switch

Accessory out, off in crank

Ign1 out, (run, dark blue) off in crank

ign2 out (resistor bypass, brown) hot only in crank

start relay signal (yellow) hot only in crank

You cannot just hook the brown or the yellow up directly, you must either use a relay or diode as I suggested, because when you release the key to run, the dark blue run voltage will feed back. This is why the brown bypass circuit is a completely separate contact --there's nothing else hooked to it, so the run voltage cannot feed back to anything.