I lied

This didn't end up being the plan at all. Too complicated for my first electrical project and way to expensive.
So I bought some single LED's on amazon (like 10 for $10) and they came with batteries, a single LED (quite bright too) and some small batteries.

I also bought a pair of calipers too to do some measuring. Some important details I have now discovered:

Max depth of the Gera Doga is 11.5mm. These LED's with their casings are a total of 14.8mm tall. After removing the casing, and just with the top of the LED, and the bottom of the battery pack, its still 12mm.

So how the hell do I shave off 5mm? I don't.

The goal now is to get little switches. I can put some wires up through the helmet of the model to the back of the neck. Doesn't interfere with movement either other than the tilt of the neck. Not a big problem.

From there, I can attach a wire to a little switch, so then I have external control over the LED. Wire it to the ground of the LED and battery pack and boom. Perfect.

Unforunatly I am going to have to use a bit of hot glue or something similar to keep everything together. However I have some gels coming too.