The light system uses a switch, it's either open or closed. No resistance to check. If you're in question about the light working turn the key on and pull the connector from the switch and ground it with a jumper. the light should come on. Make sure you have a good connection to ground. If not, check the bulb. The light systems would come on at a pretty hot temp, about 245 or so. And to address this now, the light does not come on when you start the car and go off like the oil and gen lights. Only in an overheat condition.
Jeff, If it is a on/off switch, why would the light glow dimly at all times while driving, but come on brightly when the ignition switch is on but the engine is not running?
Probably have a bad ground in the circuit board, not uncommon when they get 40 years old. I had a similar situation with the right turn signal glowing all the time and when I replaced the circuit board, problem solved.
Did you try my test mentioned above?
Also, the connector should be a 1 terminal spade type. Not the button type connector. You may have an incorrect sender.
The light did work correctly until I had the engine rebuilt. The rebuild shop threw out the old sending unit and replaced it with a new one (one connector). That's when the light glow started.
