On my new to me 2000 6x4 my cooling fan comes on as soon as the ignition switch is turned on if the engine is cold or hot and runs as long as the switch is on, when I turn the switch off it takes a few seconds for the engine to actually shut off and the dash lites slowly go out as the engine and fan slow down, I suspect the fan has been wired directly to the ignition switch due to a bad temp switch or bad relay any insight would be helpful.