Welcome to the forum. I would guess the fan control unit to be the problem but it could be a shorted wire at the fan connection. If your light was on all the time I would have said a shorted wire down by the temp sensor but that is not the issue. You could try tapping on the unit with a handle of a screw driver, sometimes it works to make them operate correctly for a while. It is the smaller black electrical box under the front fender.