I have a 97 xj with 200,000 miles. Typically runs good. I just upgraded the cap, rotor, spark plugs wires and ignition coil to Performance Distributors screaming daemon kit. (see link) https://performancedistributors.com/product/jeep/ As a part of the upgrade, I gapped spark plugs to .6

I got everything installed. The jeep cranks right up, idles nicely, sounds good. . After testing it out and running it around the neighborhood, I go back home and pick up the wife. We get out in traffic and the thing dies at a traffic light. Cranks back up easily and we get home..... I checked all cable connections and everything seems fine. Took it out again tonight and it died, this time while the car was moving. As it was dying, it sounded like a car running out of gas(sounds like you probably think it does)
I tried to crank it and it wouldn't crank. I tried to crank it again, this time giving it heavy gas, and it cranked up. Got er home, thankfully.

In the last two years, I've cleaned the IAC, replaced the throttle position sensor. The jeep has a wierd habit of stalling but it's very random and usually months in between occurrences. Usually happens when its 100 degrees or 30 degrees......So the other thing I'm thinking about is the fuel pump. The jeep makes a winding noise coming from the back of the vehicle when giving it gas. I'm wondering if this all could be a fuel pump issue?

Any advice would be appreciated.

 

It sounds like either the fuel pump or the wiring supplying it. Years ago I had a rig that did the same thing. After a lot of searching I found a wire underneath with a bare spot in the wire insulation that would occasionally hit the frame. Typically fuel pump issues aren't intermittent. Once they start going they don't get better.