This sounds like the problem I had on a '97 Dodge Stratus... (and, yes, the ol' XJ's calipers *look* mighty familiar to me....)
I had one seize up GOOD twice... and I suspected problems a number of other times (warm wheel, hot-brake smell, etc). The second time it seized "good", I was 1000 miles from home, on a Saturday night, and planning to drive the whole way home the next day. So I was, er, visibly upset.
A friend told me the "scoop" on these Chrysler/Bendix calipers.
The calipers, with age, have problems with the fiberglas piston "bloating"... from soaking up a wee bit of fluid or such. They literally get just a thousandth or so bigger in diameter. Just enough so that WHEN THEY GET HOT, they seize in the bore.
If you drive gingerly, like I normally do... or if the ambient temp is cool enough... it will manifest itself as nothing more than an "occasional" warm brake for a long time (mine went MONTHS before I finally figured it out).
If you don't get the brakes HOT, they won't seize.
But once you DO get them warm (on a hot day, lots of stopping around-town, or whatnot), they might stick with pressure against the rotor. Then they
generate their own heat, and will not let go until they cool back to room temp.
How quickly they heat up is directly related to how hard you were pushing the brakes when they decided to seize!
The first time I smoked it, I had the car towed home... then couldn't find anything wrong with it the next morning! The second time (on vacation), I had talked to my friend who told me of the problem. After the car sat for a few hours, I drove back to the motel without any problem... then I drove 1000 miles home the next day (only touching the brakes SEVEN TIMES between Savannah and Pittsburgh... and not a single time in S.C.!!!)
A bugger to diagnose if you haven't seen it before. The easy fix is a new set of calipers. I chose new car instead... so I can't report that the issue was ever resolved!! I know now that the new car was the WRONG fix. I ended up getting rid of IT after two short years... because it had more problems NEW than the Stratus did at 100k....
Den