I would start thinking it was an electrical issue. With the tractor off, but the key in the run position, disconnect the white wire (359) from the temperature sensor/sender. Ground that wire to the clean spot on the engine and the gauge should go to hot. If this works the gauge is good. Ohm test the sensor/sender. You could take the sensor/sender out and do this in a glass of water at various temps I have include what the ohm readings should be at various temps. If this looks good and you have never changed the coolant now would be a good time. I have include a link to the owners manual Section : 135 on flushing the coolant system. I have read in other threads getting out that tube on the thermostat is hard to do, there is a cap screw hold the tube in place. The tube just pulls out of the thermostat. The manual does not say to do this, but I would replace the gasket part # R502814, to avoid a leak.
When I drain my coolant, I put a plastic hose on the radiator drain plug and put the other end in a gallon milk jug worked great, filled 2 of them and the county dump took them.
60C (140F) 134 13.5 ohms
90C (194F) 51.2 4.3 ohms
100C (212F) 38.5 3.0 ohms
http://manuals.deere.com/omview/OMRE72817_19/?tM=FR