Unfortunately, my tractor is out at the farm so I can't put eyes on the engine directly and give you a description. From the shop manual, though, there are two coolant temp sensors... one for the glow plug system, which you don't want, and the other for the temp gauge. The glow plug one is part of the thermostat assembly... until I look at the engine, I don't know where the other one is.
The wire from the temp gauge should be white/yellow in the wiring harness. Maybe you can trace it down from the console to the engine.
Once you locate the sender, you can check it with an ohmmeter. Per the manual, you are looking for:
122 deg F = approx. 149 ohms
176 deg F = approx. 50 ohms
248 deg F = approx. 16 ohms
Good luck!