The fan motor and fan switch unfortunately runs directly through the ignition switch with no relay.
First, immediately stop using the fan as it sounds like you have a breaking or broken wire and thus a potential dead short and vehicle fire !!!
Then if you are a mechanically and electrically inclined, you should be able to disconnect the battery and remove the shroud around the steering wheel in order to inspect the switch and wiring more closely to see what need repairing or replacing.
I am sure that someone here may well be able to chime in with exactly what color wire you are looking for,