I bet the sender is worn out. The live gauge in my 84 190D is always on point. Nice and smooth, accurate, immediate reading. The electric one in my 85 190D is twitchy, not perfectly accurate, and I hate how it doesn't sit at 0 perfectly like the live one does when KOEoff.
Throw a new sensor on it and see what happens. If you had no oil pressure for real, you'd hear it and the engine wouldn't last long at all.