Hello I will help you with your question,
The stepper motor for the gauge has failed and you will need to replace the cluster.
GM has issued this TSB on this problem, this is a TSB about noise but note the line that refers to replacing the cluster for a functionality problem. Of course I would check the coolant level just to be sure.
Let me know what I can do to help you with this
The light would come on if the gauge went to the extreme limit so if the radiator is full you are looking at replacing the cluster. The cluster would have to be programmed with the mileage so it needs to be done by a shop with a Tech 2 scantool.
ENGINE COOLANT TEMPERATURE GAGE The IPC displays the engine coolant temperature as determined by the PCM. The IPC receives a class 2 message from the PCM indicating the engine coolant temperature. The engine coolant temperature gage defaults to 60°C (140°F) or below if:
So a high reading is not a communication problem
The track record for these clusters is not good so the gauge motor is your problem.