2nd that!
If you can't trust your sensors, at least make sure you're not running it hot or even seriously overheating it every time you drive!
Next time it's been sitting a little, pour some coolant straight into the radiator. Hopefully, it'll fill up very quickly, meaning you haven't been driving all this time without coolant!
Then fill the reservoir to the cold mark.
After you know you have coolant and know you can probably drive it,
Then I guess just swap the sensors out and see what happens.
I presume the coolant level sensor is in the overflow tank, often is. Obviously that didn't work for you, if you have one (I don't on my car). The temperature sensor is one of the two sensors in the lower intake in the front of the engine. One's for the computer, one's for you, I don't know which is which. It's right on top, I'd have to check and see how hard they are to get to. I think you can probably get your socket in between the distributor and the upper intake and pull them without pulling a bunch of other things.
Since you were wondering. I don't know exactly how they work, but I think many of the gauges use coiled wire around the needle and the magnetic field generated by the voltage running through those wires. The sensors themselves are often variable resistors, if they're true sensors and not switches, so they vary the voltage running to the coiled wire around the gauge's needle. How much force this generates must oppose either a spring or a fixed magnet to then show you your reading.
I just installed an oil pressure gauge that's being fed with 10V and not the 13+V you get when an alternator is running. Unsurprisingly, it reads low as a result.
But anyway, I also had the instrument cluster removed for some other work, and when there's no power to it, the needles can flop around any way they like; temperature, speedometer, etc.
What it says when the engine is off and there's no power to the gauge is really meaningless.
It might still work with the key in accessory though-- if the gauge gets power then.
