And requires me to remember to get up and hang it before a scheduled meeting. Or not hang it when someone calls me and a meeting erupts. And I need to remember to take it down after each call. (If I don’t, then it’s just up all the time and might be taken as seriously as a Prop 65 Warning.)
And I'm sure you've set up all the systems that make sure the complicated system is actually working and not dead weight or doing something unintended.
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.
Automations are really nice for certain things!