Welcome to '02ing! Sounds like, and looks like, you got a good one.
You're correct to be concerned about temperature indications. You really don't want to overheat that engine. The '02 temperature gauge is a known weak link in the electrical system due to poor grounding between the cluster and the chassis that deteriorates over time. Normally, it will show about the 3 o'clock position when warmed up. You state that turning on the headlights changes the temperature indication, and that is a "good" sign that the problem is caused by grounding (earth) issues. Actuating the blinkers may cause the needle to jump also. There are numerous forum conversations about this. Fixing it is not difficult, and can be quite gratifying.
You can try to improve the voltage regulator grounding by cleaning up the regulator mounting screw. The regulator (if it is still present, assuming original alternator is still there) is mounted on the inner fender near the battery.
Hot coolant enters the radiator from the cylinder head at the top, so the temperature there should be the maximum, as you guessed. If there is a possibility of air entrapment in the system, try raising the front wheels slightly and run the engine with the heater on and the radiator cap off to fully purge trapped air. The heater controls adjust coolant flow through the heater core. That's a whole 'nother project...
Good luck with your "new" '02!
Jerry