I have a 2003 Hummer H2 with an oil pressure gauge issue. The gauge randomly jumps all over the place, and will occasionally state: "Low Oil Pressure" in the display readout. I have some electronics experience, so I replaced all of the stepper motors in the instrument cluster. Did not help; issue remains. I had a GM dealer diagnose it, and they said they were not getting a correct readout from the oil pressure sender. I had them replace the pressure sender. Did not help; issue remains. They also checked the oil pressure with a manual gauge at the oil filter, and my oil pressure is fine. I found a decent price on a reman instrument cluster, so I decided to replace. Did not help; issue remains. Anyone have any thoughts on this? This has been going on for several years, so I know it's not the particular oil or filter.

 

Good start would be to check and clean all Negative terminal grounds terminal to metal contact starting at the battery and then all the smaller ones chassis to body and motor to fire wall and frame to body, few of them under the vehicle by the doors.

 

When I got my first H2 in 05 I had some interesting electrical issue with it, service 4wd, volt meter always showing lower then normal voltage and some others, After digging into it a bit I found there were no braided ground straps between the engine and the frame or frame to body. I installed a number of straps, one from the alternator directly to the frame and one at the back of the firewall directly to the frame and I also replaced the negative battery cable as it looked like it didn't have a good crimp on it. This resolved all my problems.. Looking at the picture of your front bumper it looks like you might live in a state that has high humidity or your in the salt belt.

Checking all of your electrical connection to the battery as well as what I mentioned above would be a good starting point. Based on the information you provided I doubt you have any problems with the engine.