The random pegging at 80 makes me think the problem lies with the oil pressure sensor.
I have had to change mine out in my 2004 a time or two.
It would not be unreasonable to assume the one in your 2004 might be due, as well.
It is always a possibility that the stepper motor in your cluster may be going bad, but I would lean more toward the oil pressure sensor.
With the proper sensor socket, a swivel and a couple of extensions, the sensor can be changed out in less than an hour with a couple of soft drink breaks along the way.
I would advise only purchasing an ACDelco OE (not the lower quality ACDelco Professional version) oil pressure sensor as opposed to a cheaper aftermarket unit.
I have had better luck with the ACDelco OE parts for this repair.
Your 2004 engine will NOT have the plastic filter screen that you will see some people advise you to also replace, so don't bother looking for or purchasing a replacement part for that.
Best of luck with your repair.