obviously you need a remote motor that spins the sign to "do not disturb" when the meeting starts and then back around when it's over. and a sensor to verify it's in the correct orientation.
so you get the simplicity of the sign with the automation desired by the OP.
A webcam in the corridor that shows your office door from the outside, machine vision reads the image to know which orientation the sign is in. If a meeting begins and the sign is wrong, a little LED on the desk starts flashing red.
An alternative would be to spin the sign constantly around its center of mass while a meeting is in progress.
The meeting state coheres when the sign is observed.