Not too difficult... That is, if you can find it. I have a '96 Jeep GC Ltd & my oil pressure sending unit was located at the back of the intake manifold by the distributor cap. !!!Pain in the Ass!!!
If you suspect the sending unit may be faulty just replace it with a new one, they are not expensive but a little difficult to remove and replace.
http://www.partstrain.com/
The plug or sensor above the oil filter on a 1996 Cherokee is the oil pressure sending unit. This sensor controls the oil pressure gauge.
It developed an leak and then for whatever reason sealed itself. Replace the oil pressure sending unit.
Remove oil sending unit and replace with a mechanical gauge
If it is leaking it is defective. If not then all you can do is just replace it and see if they fixes the problem. I keep a mechanical oil pressure gauge, some plastic line, assorted fittings and adapters all in a small box for testing engine oil pressure. If it is difficult to get to the sending unit, then just replace it as stated above.
Passengers side of the engine, right above the oil filter.
The oil pressure sending unit is located right above the oil filter.
We need to know which sending unit you speak of. There are several on that vehicle such as temperature sending unit, oil pressure sending unit and fuel gauge sending unit.
The oil pressure sensor is on the top rear of the engine, next to the distributor.
Replace oil sending unit with a manual gauge
It's a 30 dollar part. The unit should be located near the filter. Unplug/Unscrew the old one and insert new and plug in.