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ok. next step is to check the wiring. the sender is a grounding unit.
with ignition on put a volt meter in the circuit going to the sender. positive to the wire, negative to the sender.
if no voltage there is a short in the wiring somewhere.
when the gauge shows overheat, it is getting a zero resistance reading from the sender.
when it is showing cold it is getting infinite resistance from the sender.
or you can open the dash and probe the wires on the gauge. one should have around 6 volts as the constant regulator pulses.
the other one goes to the sender. if you pull the wire off the gauge and it goes cold, there is a short in the wire to the sender.
if it stays overheat with the ground wire off, the gauge is bad.