I had the same problem a few years back and it was the oil pressure sender. It was easy and inexpensive to replace. Deanyel is right about the harness to the oil pressure sender...the insulation was flaking and crumbling...about 2 inches of the wire leading up to the sender crumbled as I took it off. Used electrical tape and silicon spray to "fix" the harness. It's been about three years and it's still ok.

My 1995 E320 wagon has shown no oil pressure for two years. The gauge reads normally when cold, but 5-10 minutes later, I get zero at idle, and 2.5 to 3 above 1500 prm.
If you let it sit and idle for 5 minutes you would expect a lot of niose, at least lifter noise. not the case.
Most likely it is the sender unit. The shop told me the sender is a ***** to get at, so I decided to foregt about it. Two years later, with 191k on this car, it runs great. I suppose this will be an issue when I sell the car.
Until then, Don't Worry; Be Happy.