Could be the motor on it is busted. Or stuck! Mine is broken on my chevy Avalanche. You might be able to get that part of your instrument panel fixed. But worst case scenario is what I have to do. Take it to your local Chevy dealer and have the whole instrument cluster replaced.
There is and rpm sensor,on the block,check it first before tearing your dash out.
Could be many things. Loose or broken wire, bad tach guage, bad dash panel PC board, fuse, or several other things. To fix it you need to determine if the rpm sensor (TST suggestion) is functioning and then move through the outbound circuit to see where you loose the signal but do the easy things first like the fuse on that circuit.
Check crankshaft position sensor
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