I assume when you unplug it, the blower goes off? We're talking about the blower in the furnace, and not the overhead ACs right? If, so i'm thoroughly confused as the Furnace is 100% 12VDC, not 120VAC...
I assume that plugged into a different outlet you do not have this issue, such as a campground pedestal? You might want to look at how that outlet is wired. It should be wired like this...
https://www.rvtravel.com/rv-electric...p-home-outlet/