The coolant level sensor is in the coolant reservoir and is a fairly high-failure item. Temporarily unplug the sensor and see if the light goes out. If it does and comes on when connected and with the reservoir full, I would bet on the sensor. Unfortunately, I think you have to buy the reservoir to get the sensor.
Tank assembly at GM $ouch. Tank assembly at eBay: about $125 GM will NOT sell you the sensor. Some folks reported success with the $20 FLS16 Coolant Level Sensor (about $13 on eBay http://www.ebay.com/itm/Engine-Coolant-Level-Sensor-Standard-FLS-16-/331733944237 ). The FLS16 sensor is reported to be slightly longer requiring more care when reconnecting the harness plug.