If you or a friend has access to a good, modern digital multimeter, it may have a thermocouple and you could fashion some sort of rubber plug - like a lab stopper - and measure the temperature, eliminating the gauge as the culprit.

You might use a meat thermometer.

However about 35 years ago I was driving a 1956 Maxim fire engine and I saw its temperature gauge go past hot and all the way around to 0!!!

We did some investigating and found that the radiator was completely full of water and the pressure was moving the needle.

Most pumps have accessory water heat exchangers that use firefighting water and emergency water fills to cope with cooling issues if the pump can not be shut down endangering men in a fire building.

The emergency fill valve was leaking, over filling the radiator.

The sensor in your car is mechanical,

If your gauge is accurate, I would change the thermostat. Some times they are installed upside down, hiding the sensor from the hot water.

Who rebuilt the engine? Did they replace or look at the water pump? Some do rust out enough to lose pumping power. This would not account for the temperature going up and down

I
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'96 855R,'64 PV544 driver, '67 P1800 basket case, '12 XC70, the first three are mine, heh, heh, 525,000 miles put on 10 bricks