2000 Cadillac Seville Temp Guage Freaking Out

If it affects the way it is running, that rules out the cluster. It is possible you have a failing temperature sensor, terminals or connections, an ecm, or circuitry. If you know your way around a multimeter, check the resistance of the wiring from the ECT to the ECM for opens/shorts/high resistance. Did this happen after repairs like a coolant pump housing reseal, or something involving trans removal?

Do you have, and know how to use a multimeter, more specifically measure resistance.

Finding a suspected electrical fault almost requires the use of one. You have a circuit that is inaccessible, for the most part, other that the terminals at each end. It is quite possible that you have a break in the wiring, that could be inside the insulation, the wire would look fine to the naked eye. You could also have loose terminal tension at one end or the other that could cause a symptom like you are describing. If you replaced the sensor, and the fault still exists, the only other component in the system is the powertrain control module. I would not recommend replacing it, until you rule out the circuitry. The only possibility of ruling it out, without test equipment, would be to run new wires for the circuit. And even then, your talking about terminals and connectors that require proper disassembly and reassembly procedures.