Do not have an answer, but here are some suggestions to try and determine what the problem is. JDparts shows both a 2 wire and a 1 wire temperature sensor for the 6410. Disconnect the wire(s) from the temperature sensor, key in the run position (no need to start tractor), touched the wire to the engine/other wire the gauge should go to hot, with the wire(s) disconnected it should go to cold. Some tractors it goes just opposite of what I just said, that still indicates the gauge is good.
Call your dealer to get the ohm rating of your temperature sensor, most likely 0 ohms is cold and ? ohms is hot. The dealer should also be able to give you resistance of the temperature sensor at various temperatures and you could test it in a hot glass of water at various temperatures.
If you have some old electronics (maybe an old fence charger) pull out a 50 ohm and a 100 ohm resistor and connect it to the sensor wire(s)/ ground to engine, this way you can test the gauge for accuracy. Or you could buy the sensor.