It seems like I should be able to ~abuse~ use the input pullups on the Pi to drive an LED, and that means the input is open so I can also sense a switch for occasional use. I can't talk myself into or out of it, though.
If I break it into two problems, I think I can drive an LED by connecting it to +3.3v through a resistor and connecting the cathode to the GPIO. If I use a pullup it will remain off, if I use a pulldown it'll turn on. Right?
Given that, while in pullup mode, a NO switch connected from the GPIO to ground will trigger. In pulldown mode it'll do nothing.
That 'just' leaves the other parts of the problem.