We have a wall-mounted thermostat controlling furnace only, and I believe it has only two-wire control cable. I'm considering controlling the temperature of our non-ducted Coleman Mach (two knobs on the ceiling assembly) with a relay, and I'd need to run more wire and in the opposite direction than what's there. I believe I would run it surface mounted. This is one example of a conduit/molding to let you do that.

I might be able to get wire into the wall and up toward the ceiling, but the ceiling itself is "structural foam" so there's no void to run wire in. I might find a passage with OEM 120-VAC power to the A/C, but I'd guess at least the wall-to-A/C unit thermostat wiring would have to be across the ceiling surface.