2002 Cavalier Temperature Gauge Not Working?

When I scan it when the TRAC OFF light is on, it's the same code, 0118, which is "Electronic Coolant Temperature (ECT) sensor circuit high input", no matter how many times I reset it, if that fan relay is on or kicks in, it comes on. When I first start the car, it isn't on until that relay kicks in. I also checked voltage on the harness, there is 5V. So since the gauge doesn't work, I'm guessing it has something to do with that, because everything works, sounds, and looks fine, and the fan obviously comes on, so it gets the reading from the ECT sensor on the coolant pipe. The gauge just doesn't work. People have said there's another sensor that is for the gauge that is elsewhere. Does anyone know where it is? There's the two wire one at the front by the alternator which is used by the computer for the relay, and supposedly there's another maybe single wire one that has to do with the gauge? Maybe that is shorting? I don't know where it is though.

This is a great detailed answer that addresses my exact concerns. If you could find the locations for me that would be amazing. I typically do all my own car work as I'm on a very tight budget. The cav has 161k, got me across the country and gets me to auditions. I'm not going to give up on her yet.

Ok your temp indicator is a pain. I'm at work for a few days so I have limited resources. I can't find a pic anywhere for yah. It's got me stumped, for now. Back to your ECT. I usually test mine in water, heat it and check with a voltmeter. 32 F would be 10000 ohms, 86 at 2200 ohms and 212 at 176 ohms. So as your resistance goes down you get closer to a short, which would be your 5V ref to the PCM. Circuit high input. It has to be the sensor or the wiring. Maybe inspect the plug. Hope it's not worse like a PCM issue. Can your scanner read live values? If read that a dead short is around 300 F. A $5 10k ohm potentiometer would allow you to test the circuit.