Hi
So you have thought a fuel issue to change the fuel pump check valve? It could have been but it’s rare.

The coolant sensor for the computer can cause a starting problems that is more of a temperature related than a time related symptom.

From past experiences a wait time allows the fuel lines to lose rest pressure. In actuality a less volume of fuel to be available.
That amount has to be replenished by a couple tries of cranking. This is usually after an overnight length of time.

You make no mention of the fuel pressure regulator (FPR) that sends excess fuel back to the fuel tank.
They fail in two ways.

First question, If and when it does start, does run smoothly after starting?
This means no excess fuel is in the cylinders so it’s not flooding.
The rest volume of fuel probably leaked back to the fuel tank return line in that time frame.
If it’s happen regularly at five hour intervals that is a very close symptom.

The second way is the rubber diaphragm leaks off fuel into the vacuum line to it.
The fuel lies there and back up towards the manifold. The fuel gets sucked right into the intake manifold upon cranking but it runs rougher.
This can happen hot but means it was really bad before your five hour off time period.

The 1989 was the first year of the EKZ fuel injection system and a crank position sensor being used.
They become suspect at anytime if they are aged or if the cable to the sensor becomes chafed or split.

This can create a hard start problem at anytime hot or cold engine.
It can keep the fuel pumps from running or firing up very quickly by not sending a signal to the computer that turns on a system relay that you mentioned.

Unplugging the AMM shouldn’t make the CPS or fuel relay to suddenly work!
So fooling around with that doesn’t mean much IMO.

Back to the FPR, some people plug the vacuum nipple OR clamp off the FPR return line line right after shut down and wait out the time frame.
You can do one at a time
Just remember to replace them back to normal before starting.
If it changes the symptoms then you are close to finding out it’s a bad FPR.

If you buy one it’s not a wasted investment as in some day it will eventually fail.
So how old is it by chance?
111K but it’s the years that make FPRs to fail.

Phil