I have the same Jeep, 2001 4.7
I'm running Mobil 1 synthetic 5W30
When I first bought it, the oil pressure gauge would randomly drop to zero and give a CEL.
I replaced it with a Mopar unit and everything was good for 3 months. It ran at about 50-55PSI on the highway and a startup, moved with RPM's in other words, like it should. It read about 40 PSI at idle
Then one day, it went to 65PSI and stayed there. Idle, highway speed, all the time.
Something to check is when you turn the ignition on, the gauge should read zero. Don't start it, just turn the key to the on position, don't engage the starter. If you are getting 65PSI (or whatever your gauge seems to be stuck at) then your sending unit has gone bad again. I also checked all of my connections etc. My gauge read 65PSI without the motor running...
I checked gauge functionality by pushing in the odometer reset button and turning the key to the on position, then letting go of the button, your gauges will do a check and move from stop to stop.
Here's a YouTube link of someone doing that:
I also checked all of my electrical connections etc. I did have an engine code P0523... It never did give me a CEL, and it never came back again after I pulled my neg. battery terminal even though my sending unit was still buggered... don't know why.
Anyway, my dealership was nice enough to give me a new replacement Mopar sending unit after I convinced them my basically new sending unit was screwed. You can swap it out without removing the oil filter. It's tight but I did it. You have to remove your air box, then you can squeeze your fingers in there. You won't lose any oil.
FWIW... here's the 3 month old sending unit, and my newer one side by side. Different production #'s... don't know if it's something to look for or not...the NEWer one is on the left.