M y tj 2004 was doing this replaced oil pressure sensor problem solved.How many miles.
Mine dropped to zero, lights and alarms after running on the highway when all was hot. Never a problem in town. I was told new oil pump which was a $1K touch installed sp I bought a remanufactured engine instead for $1800. Which fixed all the oil leaks, returned it to as new performance and came with a 7 year warranty.
Yours might just be a sender problem.