no power to the fuel pump

I had stopped for lunch after about three hours of trail running on a hot day. When I tried to start it up it revved up really high then died and would not start again. After narrowing the problem down to loss of power to the fuel pump with the ignition on, we hot wired the pump to get it started then it ran fine all day. Now everything's back to normal. As of now when I turn on the ignition switch the pump primes then shuts off and the jeep starts up fine. Besides the question of what's wrong I would like a little education on how the fuel system works.
Is the prime (turning on the ignition) the only time the fuel pump works or does it come on intermittently?
Why doesn't it run continuously?
What tells the pump to shut off?
BTW, it's a 1989 4.0 automatic

Ok, turn the key to ON. Ignition switch provides power to the fuel pump relay, but it is the ECU that provides the ground to the relay to energize it so the power will go to the pump. The ECU kills the ground after about 1-second if the key is not turned to START or if there is no crank sensor signal received.

When the key is turned to START the starter relay provides power to the fuel pump bypassing the fuel pump relay and ballast resistor.

When the key is ON, and the engine is running from idle to just short of WOT, the ECU provides the ground to the fuel pump relay and power from the relay runs through the ballast resistor to the fuel pump.

Key ON, engine running at WOT, the o2 heater relay provides power to the fuel pump bypassing the ballast resistor.

So, engine not running, key ON the fuel pump will operate for 1-second.

All other times the pump is running, except for when the key is OFF or ACC.

Clear?

Got it! Now, let me throw you a curve ball here. My key ignition crapped out on me. Something to do with the tilt steering. In short, turning the key switch to START didn't engage the starter anymore. SO, I wired the starter to a remote switch. I still have to turn the key switch to the ON position in order to for everything to turn on and in turn everything works in that position; at least I thought it did. At first I really didn't think that was a contributor to the problem but...

As long as you wired the switch to the starter relay, and not directly to the solenoid, that shouldn't be a problem.

Now the question is if the original ignition switch has failed to the point it is no longer providing 12 volts to the fuel pump relay and B Latch relay in the ON position.

"B Latch relay in the ON position." What is this? I used a test light on the realy terminals and found ONE has power all the time, TWO has power with the key switch turned to ON and THREE sends power directly to the pump. I tested this by jumping it and listening for the pump. The other terminal (FOUR) is a mystery.

Terminal from looking at it from the pass side engine bay:

ONE

TWO FOUR

THREE