One leg of the tactile switch will wire to the '-' pin on its corresponding neopixel. The second leg of each button will get wired to a data pin on your microcontroller.
The NeoPixels will be wired in series, connected to + and - and another data pin on your microcontroller.
Get out your push button switch and flatten out all the legs. Cut off the two adjacent legs on one side. Trim the remaining two legs to about half their length and solder a short black wire and a long green wire onto these legs.
Cover each leg with a miniscule amount of heat shrink -- as little as you can get away with since we need this to fit into a very small space.
Cut a medium-length red and black wire and use your fingernail or a lighter to break and spread apart the sheilding in the middle of the wire. Thread the red wire through the + hole on the neopixel, twist it around and solder.
Solder a white wire to the "in" hole and a yellow wire to the "out" hole of each neopixel.
Trim the black wire coming from your button to about 1/2" and strip the end. Twist it neatly around the bare spot in the middle of your black wire.
Thread the black wires through the - hole on the Neopixel, twist around and solder.
Carefully bend the button around so the clicky part is pressed against the back of the neopixel. Glue it in place with E6000 or epoxy, being careful not to get the glue into the button's workings.
Thread the wires through the holes in your 3d printed cup, leaving every other hole open (you can fit 2 wires through each hole as needed).
Clip the button's wires to your Gemma running the buttoncycle test code. Your button should turn on with the first press and change colors with each subsequent press.
If everything is working, add a dab of glue inside the cup to hold the button and neopixel assembly down tight.
Repeat until all your buttons are wired, glued, and tested.