Probably a bad oil pressure sensor. In your application, its designed to turn the fuel pump relay off should it not see oil pressure.

Well that'* what I thought as well but I just put one in a few months ago. And one in just today still won't start unless it'* unplugged. Could I have some sludge build up or need some thicker oil?

Hmmm, not sure. But I'd need to look at the schematics.

it actually sounds like the sensor is shorting the power for the pump that the pcm/relay is providing. like i said the ops is a secondary redundant circuit and is only there to parallel the relay should there be a problem. in normal operation both sources supply 12v and you could lose either without the engine cutting out. but to start it again if the relay was bad you have to crank it long enough to build up oil pressure then fuel pressure would eventually come up

So how can I fix that? And where is the fuel pump relay located?

never worked on a car like yours but you need to fix the oil switch not the relay. that is obviously working. something in the switch is shorting to ground, so its either bad internally or the wires that go to it are shorting when its plugged in, look at them for bare spots touching the engine or each other