No Carl... I don't wonder. That's only one possibility. Sometimes it comes on and other times it does not.
Yes reliable way, but not on radiator. Check block. Check inlet hose vs outlet hose on Rad. Many engines are at operating temp at 195-215 deg. Isn't electric fan supposed cycle on and off depending on it's own thermostat switch? (you say it works sometimes)
What is answer as to if you have a mechanical fan?
First thing to do it check "new" temp gauge and sender in a pan of water with a kitchen thermometer. You have to be sure if it's working or not. Use the laser also, so as to calibrate it at the same time.
What
exactly makes you think it is overheating?