Why is my 2007 Chevy silverado tachometer not working?

The first thing You should do if Your 2007 Chevrolet Silverado's tachometer fails to work properly is check for diagnostic trouble codes (DTCs) with an OBD-II scan tool. DTCs might point You in the right direction, because the tach is controlled by the PCM on the white wire at pin A2. Since it's an electrical component, a DTC might give You a starting point for diagnosis. Speaking of the white wire, that's something else You should look into. Many drivers report having the same issue, which is solved with a replacement of the wire. It's somewhat expensive to replace a powertrain control module, but the wiring is much more manageable. If You're going with the shotgun method of replacing component after component, wiring is a great place to start.