Hi

Well I think you got some choices!

First I want to rule out the wiggling a temp sensor wire unless it moves the CPS wiring harness.
The CPS signal starts everything rolling with the ECU.

The ECU does nothing until it knows the engine is turning. If you wiggled it to an open circuit then the car shuts down! The next time it is running, I would get out there a shake the harness of the CPS only! Look to see where it is going. It will be behind the engine and at another point where it heads towards the cabin.
Shake it, like you would, if it had one last drop of pee in the end of it. A little shake and a little stretching if need be! (:-)

The following you can do in any order you want to get back to the above test of the CPS.

If you want to get it running you can bypass the system relay by jumping fuse 4 & 6 on the door fuse panel.
This will make both pumps run continuously and it should start and run everytime you crank it.

That almost confirms the pumps are good and not sticking.
Do the procedure several times to help rule out the pumps failure to run or start with the jumper.
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After this you can remove the jumpers permanently. If it fails to start or tries to fool you again, you should go to the relay and take it apart and close those contacts with a rubber band.

This will make the car do as before because you have closed the relay. So the pumps will run and the car should start.
Only difference you get to observe the system from the driver seat while looking at the relay under the glove box.

While the car is running undo the rubber bands that close the relay contact. The car will die.
Try an immediate restart and watch the relay contacts. Both should close on pre prime cycle from the ECU and then close again when you crank or bump crank the engine.
Put a bright light on them as they are tiny!

There are two contacts sets. One runs the main pump and the other one allows the fuel injectors to fire and put gasoline into the cylinders.

In other words, the system relay is a "main" middle man but he only works if he is told too!
He has those two ways to take a day off though! It can be a coffee break on the side of the road or a driveway holding pattern, if it feels it wants to be nice to you! (:-)

Sometimes it's a bad solder joint or the magnetic coil gets aged and starts overheating. It loses strength and drops until it cools off.

A Classic shut off and it restarts later can still be the pumps as they get old and do the some of the same things! That's why it called the process of elimination!

It best to carry a spare relay in the car! They are small but the pumps are not but can be an optional backup. I know not, of many who do that!

That's including me! At the first sign of not hearing them hum, I'm done with them! Usually past 200k though!

I hope this helps you and hopefully it was somewhat entertaining, up to the point of you, not me, having to go work on the car! (:-)

Phil