[Blas]

The switch on the dash is a second manual ground source to the fan relays. The primary ground source for the fan relays is the temp switch on the lower left side of the radiator. When that temp switch reaches a preset temp, it closes and sends a ground signal to the fan relays trigger circuit and the fans turn on. Same as you would do with the manual fan switch except the manual switch will run the fans till the battery is dead the temp switch won’t. The manual fan switch works regardless of temperature or ignition switch position.
You can replace the temp switch without removing the shroud but you may need to trim a little fiberglass to allow access with a deep well socket. I would first take it out of the circuit when the fans are running incorrectly to see if that is the source of the ground signal. Then do the same for the manual switch on the dash.if removing one or both does not stop the fans I would replace both the fan relays being careful to get the correct style relays. Take a photo of the wiring, remove a relay and take it to the parts store. I hand heard of fans coming on after wash a car before, I am assuming the fuse panel was not drenched in the process. My money is on the relays unless water played a part.