Have had the same problem. The "else weird happening" yes from me, temp, oil and clock have been all over the place. Clock behind, oil and temp not reading right. Clock I wrote off to age and just re-set her and say "Hang in there baby" as for the earl and temp, after it dies and the restart, temp and oil are not consistent.
Was thinking Nutter Bypass might help here. Not sure.
When I get to my destination shut it off and do some errands (15-30mins) and come back, starts right up and all is good in the jeep world.
Any further help be grand. Thanks yjheep for the push.
1990 YJ 4.2L 163K on it. Mechanical upgrades that I know of: brakes and lines in April. Alternator and battery both done in August.