Temp gauge on dash fluctuates up and down

An accurate temperature gauge will always fluctuate because the temperature in the engine fluctuates.

Usually the only time this is really noticeable is when the engine has been working hard and suddenly has to wait at a junction or similar and the gauge can rise considerably.

You didn't mention by how much the gauge fluctuates?
As long as it remains approximately in the normal zone it is acceptable but if it climbs into the hot zone or falls into the cold zone it is not acceptable and the cause should be investigated as soon as possible.

there are two things that can be wrong here.
1-wiring or the sensor itself may be bad.
2-you have a bad head gasket(not blown all the way)but starting to go therefore the fluctuation on the gauge itself.
does it go down when you give it gas? does it uses coolant with out leaking? let me know

probably a faulty temperature sender unit
temp sensor unit which controls the fan)

Have you checked the temperature sending unit to the computer?

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These details will help.
Thanks.

You have a Cold starting sequence that is similar to a choke. This system relies on getting a temperature signal back to the Computer. It should have at least 1 water sensor. Sometimes there are 2 sensors with one working the dash gauge and the other working the Cold start sequence. If you find 2 sensors just unplug 1 at a time and do this when the engine temperature has been rising. When you find the dash gauge sensor you will lose the reading on the dash gauge when it is unplugged. The remaining sensor would control the Cold start sequence, so replace that sensor.

Here's the thing. The ECU will shut down AC if the engine temperature is too hot. If the coolant temperature sensor is malfunctioning (lying to the ECU) telling it that the temperature is hotter than it actually is, the computer will turn the AC OFF.

You can remove the thermostat and put in a pot of water and boil it.(should open near the stamped temp on yours, 195f) From what you have posted, ti seems that you have a partially obstructed radiator core and at present, it's just bad enough for the electric fan to deal with it. (you can actually see that the temperature fluctuations happen when the fan is on and off) If you do not clean out the radiator, eventually the fan will not be enough to lower the temp and it will begin to actually go into overheat.

Check your cooling fans to insure they are working to cool the radiator...

I’m happy to assist further over the phone at https://www.6ya.com/expert/joe_a3369546f8067589

try a new radiator cap, it might old and not holding pressure