'89 fan relay? Fan on all the time

Have a new-to-me 89 Pao.
The fan turns on any time the ignition is on. Found that the fan is hot wired to a side of the coil, so obviously the thermostat switch or something else is wrong.
Any tips what to check?
Where to find the thermostat switch?
Should I just rewire in an aftermarket thermo switch?

As a follow-up, I removed the thermostat fan switch from the bottom of the radiator, connected an ohmmeter to the leads, and put it in water on the stove with a thermometer. It popped open around 185 degrees Fahrenheit. So I cut the hot wire to the fan, and let the engine sit at idle. It took a long time, but finally the electric fan came on.
The temperature gauge has never gone above midway. This might change in the summer, but the hottest it has been around here is around 70 degrees Fahrenheit, but mostly around 50.
I still don't understand why they would have hot-wired the fan when the factory fan thermostat switch was working perfectly well.