It may be a dash heat blower fan dragging on its housing. I don't have experience with that happening on our Beaver, and don't know exactly how things are arranged under the dash, but what you describe did happen on our old Pace Arrow, which had a "standard" automobile blower setup. The fan motor was worn or somehow out of whack, as best as I can recall, and I just replaced it. Some configurations have an air or motor driven shutter door that opens and closes with heater activation; if motor driven and the mechanism has loosened, worn, or otherwise failed, gears may be slipping and grinding.
Those would be the first places I'd check, so obviously does the noise occur when you make sure the dash heat/defrost is off? If not, cross your fingers it's just loose screws on a motor/fan housing setup.
Another possibility, which also occured on our old Pace Arrow, is slippage in the wiper motor drive(s), but that would be more obvious, happening only with the wiper switch on, unless there was a short circuit.
OK, Guys, what other ignition "On"-activated, under dash motors am I missing?
-Joel