Motorized rotary switch

It's possible to get motorised fader controls that present essentially the same problem, so I'm sure there is a solution.

How determined are you to retain a physical rotary switch? It ought to be possible to design a ratchet system that enables you to nudge the switch left or right one position at a time while still allowing manual control. But it might be tricky to design and build.

Perhaps a better approach would be to separate the manual input from the position display. I mean have a position indicator which is controlled electronically (digital display, or physical dial/gauge moved by a stepper motor/servo etc) and then have a separate rotary encoder/switch which the user can move to trigger the controller to change the switch position. So the user can trigger a change by spinning the dial, but the controller can also do it spontaneously, and both of these use the same mechanism.