This is exposed and the fan is some sort of selector switch? The selector switch can be removed and replaced with a relay. Question is what is the hp or power draw of the fan? You’ll need a relay that is designed for an inductive load.
That would be what I would use because it’s built to work with inductive fans and that is an important distinction. In fact, I’m going to end up with a spare of those very soon as I’m replacing my Sonoff fan controller with an Inovelli Zigbee - so if you want one cheap you could buy mine, it’s already flashed with ESPHome.
Hey @byronmorrison kiwi here to. Did you get anywhere with this? I have been thinking of doing something like this between our main lounge area (with an in wall wood burner) and our main bedroom - with the thought that I can pump heat in winter from the lounge to the bedroom and also extract warm are from the bedroom to the lounge during the summer.