I would suggest checking voltages, starting at the battery (check the battery clamps and posts, are they clean and tight).
With the vehicle running, stress test all the under the hood wires, too see if moving them causes any problems. You need to dig up an FSM for troubleshooting the 4 cylinder. Very few of us here have a 4 banger, and that year was a transition year, throttle body injector, with a bunch of special valves, that less than a handful of XJs here have. Also check for any call backs TSBs I think they call them, that might be related to your problem.
There maybe an idle reset procedure in the throttle body version that is not resetting a valve properly. The 87-90 Renix 4.0 l, needs 6-7 seconds of off time to reset, something called a B+ relay is involved, IIRC.
Even though it is a single fuel injector, throttle body injection (that is what you have right?), I would still look for a leaky injector partially floodding the engine on start up? Aslo look into those other valves the 2.5 L throttle body system used.
Search for threads here about the "throttle body injection" (use as key words in google with
, or search here) for the other guy(s?) that has one of these beasts still running! And PM him to join us in this thread.