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From what you are describing, it sounds like you are going to have a fault in the Coolant Level Sensor/Module. These level sensors are a "known problem" and GM has issued a Technical Service Bulletin stating that the most common problem associated with this is contamination of the coolant, and that contaminated coolant interfering with the proper operation of the sensor. The best bet at this point is to have the cooling system flushed and refilled, and then replace the sensor. It's mounted to the passenger's side of the radiator.