OK Jamie, you're in my wheelhouse now. I sell sensors for a living.
The sensing element used in these types of coolant temperature sensors is a device called a thermistor.
The characteristic of the thermistor that is used to infer temperature is the fact that it's resistance changes with temperature. Apply a stable, known voltage to the sensor (like 12Vdc, look at the voltage drop across it (with respect to ground) with a voltmeter (which is what your coolant temperature gauge is) and your off to the races.
Refer to
https://en.wikipedia.org/wiki/Thermistor and you will be an expert on the subject, LOL.
So what does all of this have to do with checking to see if your sensor is good or bad? A couple of things:
1. Remember I said apply a stable, known voltage? If you're not doing this due to lack of input voltage regulation, or a bad/poorly connected +ve, output, or negative (remember the case of the sensor is the ground connection) electrical connection the results could be off. Start there.
2. Then the next thing you can check is what values of resistance the thermistor outputs at various temperatures. There are charts out there you can look up, but this is where the car OEMs and sensor companies do a poor job of documenting what's what. Due to reasons of economy, they're not that consistent in resistance output at a given temperature from unit to unit.
Armed with this knowledge you can still go poking around and check the resistance across all of the coolant temp sensors in the system (with a digital multimeter set to ohms) to see how they compare, both to the published chart(s) and each other.
I hope this helps.