furnace

It certainly sounds like a relay or controller with maybe a little dirt between the armature and actuator arm. Does your rig have ducted heat and AC? There may be a door than directs the air flow and is just not quite making it opened or closed. I'd be more concerned with the furnace not working properly than a buzz from some part of the HVAV system. The two could be connected but probably not.

I've not been much help but not being there to see and hear makes it hard to solve a mystery that people who are there can't solve.