So I have been helping my friend work on her 91 XJ. One of it's problems is it will die when you let off the gas from higher RPM's, yet it starts and idles fine (current idle is a bit high at 1500 RPM's). We have traced the vacuum lines and have not found a leak anywhere. Then I realized that when you turn the key on you do not hear the fuel pump at all, my 93' you can hear the hum when you first turn the key on. So could the pump be bad? I think I might check the wires going to the pump before I diagnose the problem (this XJ has been under water before...). What I am confused about is why does it run with a non-working fuel pump? Any help would be much appreciated.

 

Check to see if the intake manifold bolts have come loose.

Clean the throttle body and IAC after that.
Courtesy of TJWalker:

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The Idle Air Control (IAC) is mounted on the back of the throttle body. (front for 87-90) The valve controls the idle speed of the engine by controlling the amount of air flowing through the air control passage. It consists of a stepper motor that moves a pintle shaped plunger in and out of the air control passage. When the valve plunger is moved in, the air control passage flows more air which raises the idle speed. When the valve plunger is moved out, the air control passage flows less air which lowers the idle speed. Over time and miles, the IAC can get carboned up which can have an adverse affect on idle quality. Cleaning the IAC may restore proper function and is an easy procedure to perform and good preventive maintenance so it is never a bad idea.

CLEANING THE JEEP 4.0 IDLE AIR CONTROL

Remove the air filter cover, associated hoses and the rubber boot that goes from the air filter cover to the throttle body. Remove the IAC with a torx driver (2 bolts; one can be kind of hard to get to)

"Gently" wiggle out the IAC from the throttle body. Gasket on the IAC can be re-used if it is not damaged

Clean the IAC with a spray can of throttle body cleaner; inexpensive and available at any place that sells auto parts. Throttle body cleaner is recommended rather than carburetor cleaner as it is less harsh, safe for throttle body coatings and is best for this task. Use cleaner, a rag and a toothbrush and or Q-Tips. Be gentle; don’t twist or pull on the pintle that protrudes from the IAC as it is fragile and you could damage it.

Thoroughly spray clean and flush where the IAC seats in the throttle body with the same spray cleaner

It is also a good idea to clean the entire throttle body itself, the butterfly valve inside of the throttle body and all associated linkage as long as you have things disassembled

 

Wow, thanks! Sounds like a good place to start. The engine is from an 80's XJ but the rest is all 91'. I will see what my weekend looks like and hopefully make some progress on this issue, and maybe even do a few little things to my XJ too haha.