Radiator fan only turns on when my car is off?

I'm going to a mechanic tomorrow, but I'd like to have an idea of what the problem is before I go in, so they don't overcharge me for repairs I don't really need.
I have a 1992 honda accord. It has a lot of problems, but has been, for the most part, drivable. I've had problems with the fan in the past; it doesn't turn on when my a/c is on, so my car will overheat. I pretty much just ignored that though (would rather save money for a new car than spend it on a repair that isn't 100% necessary) so I just dont use the a/c. But today, I noticed my car overheating while driving. A/c was not on. So I pulled over, checked the antifreeze, etc. After playing around with it for a bit, I noticed that the radiator fan only turns on once the car is off. So the fan itself is still functional, and when the car is off, it recognizes that it's too hot. But when the car is on, the fan will not turn on, no matter how hot it gets. What do you think could be the problem?

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