Chevrolet Repair Questions? Ask a Chevy Mechanic for Answers ASAP
It sounds like the sensor on the parking brake cable is faulty or out of adjustment. I would check there first. Here is the replacement procedure:
Parking Brake Indicator Switch Replacement
Caution: Unless directed otherwise, the ignition and start switch must be in the OFF or LOCK position, and all electrical loads must be OFF before servicing any electrical component. Disconnect the negative battery cable to prevent an electrical spark should a tool or equipment come in contact with an exposed electrical terminal. Failure to follow these precautions may result in personal injury and/or damage to the vehicle or its components.
Tighten the retaining screw to 4[n-m] (35 lb in).
Tighten the negative battery cable to 15[n-m] (11 lb ft)