Drop a little superglue in the tip of the horn and slide the LED in so it stays put.
Slide the battery, then the neopixel ring into the horn. Set the charger in place with the JST connector facing downards towards the horn's base.
Then, attach the copper tape to Gemma's A1 pad. You can do this by slipping the tape through the hole and soldering, or if that's too fiddly, solder a short wire to the pad and the tape to make the connection.
Secure the charger with a dab of hot glue.
Tuck the Gemma inside the base of the horn, being careful to keep the capacitive touch pad away from any other electronics, as much as possible.
At this point, my horn went haywire. The capacitive touch was either way too sensitive, or not sensitive enough. Or, all the other pads on the Gemma would set it off but pad A1 did nothing.
I spent a good amount of time calibrating the software, testing, shielding, and reconfiguring the copper tape. The calibration here is pretty tricky. As soon as I unplugged the USB cable, the horn reacted totally differently -- without that ground from the USB port, the copper tape's sensitivity would freak out.
Don't give up! Check the calibration page in this guide for some tips.