LEDs to illuminate underside of king bed
Buy 12V LED strip lighting. Google: 3528 5050 5630 5730 7020 SMD Strip LED. (Pick one number and google that, not all at once.) eBay is a great place to get it.

The bigger the number the brighter the light, but since you probably want an entire strip running the length of the bed you might not want a bright one.

https://en.wikipedia.org/wiki/SMD_LED_Module

They are sold by the meter, or the reel - try to buy one long enough to do all 3 sides in one run.

Don't forget a power supply - make sure it's powerful enough, the strip lighting is rated in Watts (or Amps) per meter. You can pug it into a simple wall timer.

Some of them come with pre-attached sticky tape on the back. You may want to consider getting a waterproof one if the LEDs will be exposed since the waterproofing also protects it from anyone touching it.