I run a Carter 4600 that I bought from @mudski years ago. It uses the old TB45E ECU “prime” function to run for 5 seconds on ignition, which is basically while the glow is happening, then switches on full time once oil pressure is established.
If engine stalls and oil pressure drops, the pump just stops.
Some command it from the alternator to have a similar cutout feature if engine stops for whatever reason.