Oil Pressure & "Part Time"

I have a line on a 99 XJ with 135k, but there's two things I'm unsure of.

1 - Oil Pressure Gauge fluctuates, oil level in engine is fine. Sending Unit?

2 - Says "part time" on the dash, dealer that has it can't get that to go off and be just in 2wd. Transfer case? Thanks in advance.

Fluctuates when ? How ? 10-20 psi at idle and 40-60 psi at 60 mph is the normal range. The pressure will go up and down with rpm's. Faulty senders and damaged wires are not uncommon.

Is it in 4wd or is the light just on ? Does the 4wd hi and low both work ? Have you adjusted and lubricated the 4x4 shifter mechanism ? The 4wd indicator lamp switch on the T-case can fail and is easily replaced.

Test drive it in 2WD, and take a sharp corner on pavement. If it behaves, and doesn't pulsate and scrub tires, it's in 2WD and the switch is bad. Easy fix if so.