Using a relay is imparitive on the cooling fans but it sounds like your problem is going to be the switch itself..It's going to be located about half way down the column and retained by two screws with two gangs of wires plugged into it.The dimmer switch will share one of the screws.Have you checked to see if the blowers run with the key in the acc position?? Some folks wire them that way to avoid engine run-on when you shut the engine off(relay fixes that too)