[dmjlambert]

Rust_never_sleeps is right, no circuitry in common at the fan switch. The ignition switch is what the radio, turn signals, and fan have in common. I think it is likely when you push on the terminals of the fan switch you are actually disturbing the terminals of the ignition switch, which is right next to the fan switch. In particular, the 12 ga brown wire which provides accessory power from the ignition switch to radio, fan, turn signals, etc. So, check that the brown wire terminal in the ignition switch plastic connector is fully seated and in good condition. In 67 and possibly early 68 if you have no 12 ga brown wire, it is the 12 ga pink wire that provides power to accessories. Most of 68 through 72 use the 12 ga brown wire.

A stock radio would normally be connected to the Radio position of the fuse box, but somebody could move the plug-in connector from Radio to CIG if they want the radio to operate without the ignition switch turned on, because CIG is always hot.