12 V Led inside light strip.

Here is the other slide with LED strip across the top. All the other lights you can see are LED bulbs also.

BTW, I also use a backlit NOOK HD+ for most of my reading, and get thousands of free books via my local public library with the Tennessee READS program and Overdrive. I can access the library from anywhere in the US where I have internet access.

I have not seen the white only strips with a remote. The only ones I have seen with a remote are the color ones, and they have a separate control box between the power source and the light strip. Also the color strips have a four wire connector whereas the white ones only have two. For a power source, anywhere you can find 12v will do. in my case, I put a strip on the top or the slides, which throws indirect light off the ceiling. For the bedroom, we had a 12v lamp on each side of the bed, so I just tapped into the wiring at the light, and ran a small wire up to the light strip. In our case, I was able just to cover the short wire with white tape, and it is almost invisible. Here are a couple of pictures that might give you ideas..
You can see wire from light up to the strip in this picture


leftover two-inch piece of led strip

I solved my late night reading a few years ago by switching to eBooks on my smart phone while camping, then eventually bought a Kindle Paperwhite which was even better since it works in bright sunlight as well as in the dark and runs a week or more between charges.

When we bought a newer camper a couple of years ago we didn't even put reading lights in the bed area.

PS: I mostly read free and very cheap books from Amazon.

John with remote/3-way that sounds ideal sounds ideal. I need it for late night reading without draining the battery. What is the best way to connect to the battery? Any caveats on overload, wiring.

Look at the bottom of amazon listing.
For just few more bucks you can buy remote.
Maybe overkill for OP application, but as I mention, I have color light under my 6 foot long range shelf.
From the distance at my nook table I can turn on/off, change colors, variety and brightness.
The color strip has white option, but it is white that comes from combination of 3 colors, not the pure white.
Probably not the best for reading.

Take a look at this. If you want to cut the strips, you can bet a small package of connectors that do not require soldering.

Rotary switch

My white led strips seem to be plenty bright. I have used the multicolored ones, but they do not seem to be as bright, and the white is kinda off. They can be zigzagged, being careful with the bends, but I would cut strips and connect in parallel. then you could use a common rotary switch for a three way bulb, and have a choice of brightness,

I bought the strip from Amazon as well, but don't think it is powerful enough for what OP wants and zigzagging 16' might not be the best solution.
I have the long one with multicolors attached under commercial range shelf, so when DW cooks she can see it better in colors ;)
Pay attention to descriptions as too often seller give you "incandescent equivalent"
I read the actual power and per my experience 5W of LED is marginal, while 7 is most likely. 10W single bulb will give pretty strong light.

Look at these. can be cut to whatever length you need, might use two strips side by side for even more light. I have several in our MH, powered from available 12v source.

Led Light Strips