I'm looking for something like a doorbell indicator that can display either "Come In" or "Busy" when someone approaches my office. It should be controllable from an app or a wireless button in the room, with the signal working through a wall rather than requiring line of sight like a television remote. The goal is to communicate with a deaf family member while I'm on a video call without interrupting the call. Ideally, the solution should cost no more than $50.
3 Answers
The simplest solution is a lamp or illuminated sign outside the office with a color-changing smart bulb. Use green for “Come In” and red for “Busy,” then control it with a phone app or a wireless smart button. A two-button setup would make switching between the two states quick and clear.
A fully self-contained door-mounted display probably isn’t common at this price, but a small home-automation setup could work. A smart light or display outside the door can be controlled from a button inside, and automation software can connect the pieces. It’s more setup than the basic lamp solution, though, and may exceed $50 if you need several components.
You can do this cheaply with a wireless wall switch and a lamp or lightbox. Many wireless switches communicate through walls, so line of sight usually isn’t necessary. Put a printed “Come In” or “Busy” label over the light, or use different colored bulbs. This should fit comfortably under the budget.

I wasn’t sure whether wireless switches would work through walls, so that’s helpful. I don’t know much about this technology, but a simple light with clear labels sounds like the easiest option.