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Lower front of the driver's side head near the #1 plug, same place on every LS motor
FWIW, I've had an intermittent false low coolant warning twice over the last several years. The symptoms were an erratic temperature gauge accompanied by the low coolant warning even though the coolant level was OK. Both times it was caused by faults in the wires leading to the connector that attaches to the ECT sensor. Once there was a break where the wires had been sharply flexed at the connector, the second time there was a break where the wires were pinched between the alternator and the valve cover. It's an easy fix. Chevrolet parts has a replacement connector with pigtail, just cut off the bad wires and/or connector and splice in the new.