No tape, no adhesive etc. I would never attach anything to the doors.
Make the sign with a notch at top, get a clear suction cup with hook (dollar store has bags) then hang it in your window if you have one (value and moderates).
If you are in a deluxe hotel with only a hallway, no window, I agree to look at the door handle hanging kind ... treat yourself to a custom made one and then take it home as a memory.