First, I credit FJforMee for inspiring me to come up with a solution for better lighting for the backseat passengers.
I wanted to provide my rear passengers (ie., my 9 and 12 year old kids) with individual lights that would not disturb the driver, me, on long night hauls. I liked the puck light idea but wasn't crazy about the ambient light they throw in the cabin.
I decided on using a LED book light made by Mighty Bright. The light has a flexible wire coil gooseneck so you can position this light in virtually any direction. The bottom compartment houses 3 AAA batteries and has a clip that can be attached to a book. I purchased two lights and two bases that the light snaps into. The base has a strong magnet on it's underside. Lights and bases cost me $40.
For my install, I decided that I would attach the base to the plastic panel that wraps around from the rear seat window. Specifically, I wanted them slightly behind and above the cutout for the rear seatbelts - which would be about level with an adult's head. I also wanted the lights to be removeable/mobile. A light would be installed on both the passenger and driver side panels.
I decided that I would attach the lights to the panel using rare earth magnets hidden behind the panel - which would result in an invisible install. I bought two magnets ( 1.5"x.5"x.25") for under $10. For those that haven't used earth magnets, let me tell you... they are strong!
I pulled the plastic panel away from the headliner which gave me enough access to the rear of the panel to glue a magnet there, opposite to where the base would be positioned. I placed the base on the outside of the panel to ensure proper positioning and then left it there while the glue dried - essentially allowing the magnetic 'pull' to act as a proxy for having to clamp or apply pressure to the magnet while the glue dried.
Done!
The advantages of this set up are as follows:
-Rear passengers can turn the light on while in the base and postion the light exactly as they need it.
-Rear passenger can remove the light from the base and clip it onto a book for more direct lighting.
-Front passenger can also use the light and clip it unto a map, book, or the sun visor.
-The entire base can be removed, leaving no visable sign of install
-The entire base can be removed and magnetically attached to any part of your car's metal body - great for flat tires and under hood application!
-When not in use, the flexible neck can be positioned to be non-intrusive to the rear passengers.
-batteries supposedly last about 40 hours (threw an extra set in the glovebox) and LED bulbs last a long time.
I've had this installed for several weeks and can attest that the magnets hold the lights very firmly in place - even on bumpy roads. If you are concerned, you can order thicker earth magnets, which will have a greater 'pull' force on the base - don't go too strong or else the sheet metal from the car body may pull the magnets away from the inside of the panel.
My kids love the lights.
I just noticed that the Mighty Bright website no longer lists the magnetic base as an option. Maybe you can contact them for availability. Or possibly just glue a magnet to the back of the battery housing?
Might Bright in Base:

Mighty Bright with light on:

Just the base:

How strong is the earth magnet?

...and if you ever get a flat tire at night?

The actual light:
