There may be a hint to your mystery device identity in the list of other suggestions by Sense. You said Fan was the top suggestion at 46%, but what were the others? You can return to that list at any time by going to the device page, then Settings (the cog icon in top right), then the > arrow next to Name.
Sense was able to identify my bathroom exhaust fan, which has tiny blades hidden behind a grill. The bathroom fan uses 52W when in use, and Sense was 97% sure that it was a Fan. Sense also identified my kitchen exhaust hood above the stove, which again has small blades hidden inside a duct. The hood uses 200W when in use.
Your description of running for 2-3 minutes at a time every ten minutes makes me think it is something automatic. If it really is a fan, could it be an exhaust or ventilator in attic/basement/crawl space/garage?
Another way to track devices that run frequently is to turn off breakers one at a time, then wait for the mystery device to fire. If your mystery device never does, then you have at least found which circuit it is on, which may give a clue as to what or where it is.