The light is built around the smallest Arduino I could find that included LiPo charging circuitry. Luckily, I had a few Fios sitting around from back when I was enthusiastic about Xbee.
I modified the Fio slightly so it could know when it was charging (ie, when it was sat down on its base). I added a tiny greenwire between the "Charging" LED, ran it through a small resistor, and sent it to a digital input.
Note! Working with old Fios can be tricky because the microcontroller on the board changed several times. I ended up being able to flash mine by choosing "Arduino Pro Mini, 5V 8MHz" as the target board.
The animation when charging took a couple tries to get to a place I was at all satisfied with. I tried several methods to get a nice, even fade down to dark but was unable to avoid seeing really noticeable discrete steps most of the time. I haven't thought about it too much, but part of my smooth-birghtness-fading problem might be related to running the Neopixels off of a 3.7v LiPo rather than the specified 5v supply.
At any rate, a lone pixel orbiting slowly seems like it will be OK to live with. I'm hoping the people I'm making this for will be able to test it on their bedside soon, so I can work on other options before the baby comes. If I have time, I might work on making the pixel orbit in a consistent time interval that is useful, like 15 minutes, so it can be used as a timer.