According to the GK19 wiring diagram:
The (single-wire) Thermal switch is supposed to send a ground-signal to activate the Overheat Indicator light, And also the Water Temperature Warning Buzzer, when the engines coolant overheats.
So If your Overheat light stays on with with that Thermal Switch unplugged, a probable cause would be that wire has shorted to ground somewhere, or that your Temperature Warning Buzzer is defective/shorted, and back feeding a ground-signal that's causing the Overheat Light to stay on. (you could start by simply unplugging the Temp Warning Buzzer, and see if that corrects the Overheat Light problem or not...)
Or, yes you could just instal a aftermarket Temp guage and Instal Its sending unit in that same location as your old one wire Thermal Switch.
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That wiring diagram tells us the 2-wire thermal switch in your Radiator should have power to one of its wires when the Ignition switch is turned on, and then the other wire runs directly to the Radiator Fan motor(s). So you'd simply need to confirm one of those wires is receiving power with the key on, and If it is: Then you could simply jumper those 2 wires together to diagnose if the Thermal switch is defective and the only problem.
The wiring diagram doesn't show it, but I'd imagine you've got a fuse wired in somewhere to protect the cooling fan circuit...
How did you wire in your switch to turn the Radiator fans on?