Oil pressure weirdness

I have a bone-stock 99 Cherokee Sport auto with the 4.0. Recently, it wouldn't start without some gas pedal action and wouldn't idle without same until it was fully warmed. Since the battery was at the end of it's service life I replaced it and the starting issue is gone.
Everything is working normally but for the oil pressure gauge. It reads high, like 60-70 PSI, and at highway speeds it can read even higher. The normal reading is about 50 PSI and dropping a little at idle. What is going on?

Oil pressure sending unit is failing. It is located directly above the oil filter

Replace it.

Buy it DIRECTLY from the Jeep dealer for the best reliability/accuracy/mating with your factory gauge. Well worth the extra $20 or so. No lack of threads of people having trouble with some of the aftermarket units.