Note from DJ
I am sorry OP wf_s10 that all of your checking has come up with no negative results, I was hoping that something positive would turn up.
ECU failures in XJ are very rare but it looks to me that you have one; I have worked my computer a lot searching with many different combinations of words to no avail at finding some other cause for your Hot
ECU.
The only advice that I can offer you is start searching the junk yards for a replacement ECU. I am afraid that if you don’t try a replacement ECU something bad is going to happen, like the Jeep will suddenly stop and never start or some wiring is going to melt and possible cause a fire. Or if you are good at electronics you can remove the cover on your ECU and look for a hot looking spot unsolder the bad looking components and replace them. This procedure has been posted on this site in at least one occasion with success.
If you decide to go junk yard searching hear is some information that may help in your search.
Any ECU from a 1987 through 1990 is supposable compatible for your Jeep, the best one is from the 1990 model year it has the latest programing which is the same numbers you reported that you have which was the 5300 5428 this number was for the 6 Cyl. Engine, w/Auto. Trans. So that is the one you are searching for, it is slightly possible you could find that same number in an earlier Jeep, the last four digest are the most important.
If you go to a pick and pull type of junk yard this info may help in your search. Look for the VIN. Number of any Jeep that looks possible a good donor. What you are looking for is the 10 digit example being my Vin. # starts like this 1JCMT7848J the letter J is the key to the Model year, H=87, J=88, K=89 and L=90you are looking for another L mine is a J and it is a 1988.
Hope this info is of some help to you, this is the best information that I can offer, at this time.
Please post back what you do to resolve the problem or not, But I will look for a successful fix.
Here’s hoping!