I have a low mileage 1996 Polaris Sportsman 500. I have a couple issues that I suspect are related.

1. It would overheat and I noticed the fan was not coming on. Replaced the sensor near the radiator cap and still nothing. Bypassed the sensor so the fan runs all the time when the key is on. Ordered another sensor, hooked it back up, and now the fan won't cycle off. Runs all the time when the key is on. While that has helped, it still overheats when idling or running more than 30 min.
2. So I decided to change the thermostat because that is the easiest and cheapest next step before rebuilding the water pump. I was surprised to find no coolant in that hose and the area behind the thermostat dry and void of coolant. The radiator and overflow container have coolant as they should. So now I am thinking I need to rebuild the water pump. Is that the right conclusion?
3. If coolant begins to circulate properly, do you think the fan sensor will now work?6