Yes or no

On a 1990 XJ, does the fuel pump ballast resistor "tell" the fuel pump to continue to hold pressure?

If not, what is it's function. I've been getting a lot of contrary information.

it's a resistor to lower the voltage getting to the pump (after startup) to reduce noise from the pump. it can be removed, and I believe it is removed on later years.

No.

The fuel pump ballast resistor is a current-limiting device used to reduce noise transmitted through the "frame" to the driver caused by case vibration. Slightly reducing the pump's operating speed seems to reduce noise.

The ballast was added for the 1988 MY, and offered as a voluntary recall for 1987. It is possible to bypass the resistor entirely without ill effect.

The fuel pump is "latched" by the B+ relay (as I recall - I'd have to check!) which energises the fuel pump relay. The fuel pump relay may also be latched by the ECM.

Pressure, however, is held and maintained by vacuum on the fuel pressure regulator - the pump should run constantly while the engine is running.

5-90

Not to hijack but if you bypass the resistor does it make more vibes since it's original purpose was to lessen them, or was it more to reduce noise?

Just a idea, since you are loosing pressure, have you checks you gas cap?

The resistor quiets the pump down.

A bad gas cap wouldn't have a damn thing to do with low fuel pressure.

Are you sure it doesn't hold the pressure? or maybe it just never gets to the right pressure? Have you checked the fuel filter for blockage? Maybe something is shifting in there and it starts with the right pressure and than it drops cause some pos shifts in there?

If you remove the resistor it makes a little more noise and thats it. I have bypassed mine long ago. After a start and run, then die problem. It has no effect what so ever on holding pressure. If fuel pressure drops after it has been shut off for 5 minutes. Its a bad regulator. Most common symptom of a bad regulator is extended crank time. Which I think every fuel injected jeep has. It is possible that your new pump is weak. Would not be the first I have seen a new fuel pump be junk from the box. If you get chance to look at it pull the vaccuum hose off the regulator, if raw fuel comes out of the regulator.
Then you know it definately needs to be replaced. Just my .02 cents. HTH