I have a 2004 GMC Sierra that had the same problem. The stepper motors used on the gauges in that period tended to fail. I was cheap, so I just replaced the stepper motors. I bought the set to replace the stepper motors on all the gauges for under $30.
You can find good instructions for the entire process on the internet. I had one of the sites bookmarked, but that was on my old computer that expired a couple of months ago.
On my truck, the plastic cover just pops loose. As I remember, you have to tilt the steering wheel as far down as possible and have the gear shift lever as far down as possible to get enough room to wiggle the plastic cover out of the way. Once the cover is out of the way, there are four hex head screws (7mm?) that hold the instrument cluster onto the dash.
You have to disassemble the instrument cluster to get at the printed circuit board where the stepper motors are soldered onto the board.
When you replace the motors, do all the gauges at the same time. When one gauge fails, the others aren't far behind.
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