There may be a more turnkey way, but I would use a dry contact reversing switch with a DC motor driving the chain from the bottom.

I have 9 cameras installed around my home - with none of them pointed anywhere inside (except my garage). I simply cannot come up with good reason to have one inside except to monitor a pet. Nothing gets in or out without video. That’s enough.

In my opinion, people who live there should be able to preserve their own privacy in that space.