What you're thinking of is some kind of remote. The problem with a remote is the power would have to be on to the receiver all of the time, which would run down your batteries.
You could install a self contained light (similar to a closet light) where it would be easy to reach. You'd have to replace the built in batteries frequently, but the total cost would be modest enough to make it work.
Holiday Rambler Navigator DP, Hummer, and Honda VT1100C Shadow
Well, one way is to change out your reading lights to something more user friendly.
Now on the seriouse side of things. We mostly do all Boondocking. And we have two LED TV's that hardly use any power. We have also replaced all of ouur Motorhomes lights wiht LED Lights, which uses hardly any power either.
I have bought a few LED Puck-Lights. These work very well for reading, or what ever. Theyy put off quite a bit of light. And the AAA Battries lasts a very long time. We use these a lot, and it really saves on our Motorhomes Battery Bank.
Check out "Old Bob". "The Boondocker" he use a LED Head Light to read by, and uses it for many other things as well. All you really need to do, is to start thinking outside of the so called Box.
We have reading Lights on each side of our Bed, but we never use them. Because I have a Puck-Light on each side instead. You just touch it one, and it lights up on Low. Touch it again, and its oh High. The Puck-Lights also Swivels in different directions, so you can control where most of the light shines to.
There Pretty Ceap, and it really does a Fantaastic Job of saving the Motorhomes Battery Bank.
Just one of many manyy things we have done to make Boondocking even more "Enjoyable" and wvwn more "Comfortable", and not hardly using any of the Motorhomes Battery Bank either. We have our Motorhome, very well set-up for Boondocking, in many many ways.
Of coarse we have been at it for a bit over 45+ years now. So when we go Boondocking, we can stay out for quite a while before we need anything, or to dump anything.