Idea

Using a microcontroller and sensor, turn on light in closet on opening.
Components:

  1. Microcontroller
  2. Ultrasonic pinger or other proximity sensor
  3. Rechargeable battery
  4. Controllable LED light or strip.

Program the controller using the sensor, power the light on open.
Package together, maybe design and 3D print enclosure, and mount using sticky strips.