Lets get back to basics. When it fails to start do you have a good fat blue spark at the plugs?
If weak or no spark.
The starting after cooling down sounds like a faulty Hall Effect sensor in the distributor or the flywheel position sensor whichever you have.
Another candidate would be the ignition power stage (aka ignition amplifier)
If you do have a good spark at the plugs, then it looks as if you have a fuel problem.
To confirm this, try squirting some fuel or starting fluid into the manifold and
see if it will fire up. If it does, try replacing or re-soldering the fuel
pump relay or jumper it out so that you know the problem is not the relay.
If the trouble is in the fuel system I can`t really help, (K Jet experience only, not much on L Jet and none on Rex/Regina)
When trouble shooting this type of problem you need to be methodical, start with the simple things, and at least determine whether the fault is ignition or fuel first. Always check for spark first as it is so easy to do.
Good luck,
Colin.

I've had similar symptoms on my '87 when I acquired my car, but not quite as bad a yours. Here's what was wrong with my car:
-Bad Idle Air Control Valve (flooded with oil due to a clogged Flame Trap).
-Fouled spark pluges (caused by the bad IAC valve mentioned above)
-A broken vacuum line.

Also, check these items since they can also lead to symptoms that you've mentioned.
-Mintature holes in the tubing/ductwork between the Air Mass Meter and Throttle body.
-Fuel Pressure Regulator (remove vacuum line and check for smell of fuel)
-Air Mass Meter
-RPM sensor (mounted in the distributor where the wire harness connects to it, below the distributor cap).

I would feel pretty confident that your Relay and fuel pumps are not to blame for this problem. The symptoms would be very different and you'd have more problems at all driving ranges. Also, if you can tell if your car is running rich or lean, that would help us out in diagnosing the problem further. This can be done by hooking up a wire to your Oxygen Sensor and running it to a volt meter. Don't run the car with the O2 sensor disconected since this will cause the car to run rich, -so add a wire at the point where the O2 sensor wire connects to the car's harness. You should get an average of 0.5 volts or so at Idle with a warm engine. A rich condition starts climbing upwards (max value would be 0.9 volts) and a lean condition would be lower (around 0.2 or 0.1 volts).

Good luck and God bless,
Fitz Fitzgerald.

P.S. A $25 vacuum pump is a great investment in hunting leaks and diagnosing vacuum parts.
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'87 Blue 245, NA 214K