Be sure you've uploaded the code to your Pro Trinket before assembly. That will make it a lot easier to test at each step and be sure things are working.
Trim one of the side legs off your switch and trim the other legs so they're a little shorter. Solder a 4" white wire to both remaining legs and cover with heat shrink.
Trim the side legs off one side of your switch button. Flatten the remaining two legs out so the switch lies flat on your table Solder a 7" white and black wire to these two legs and cover with heat shrink.
Cut the trace between the two switch pads on the LiPoly backpack with a utility knife. Solder the two white wires coming from your switch into these two holes.
Stack the LiPoly backpack on top of the Pro Trinket using the included headers, aligned as shown. Solder the headers in place on both boards and trim the header legs close to the boards.
Plug your battery into your charger and flip the switch. The lights on the Pro Trinket should come on so you know it's working.
Solder a 7-8" red wire to +, black wire to G and white wire to "IN" on the back of the Neopixel Jewel.
Solder the white wire to pin 5 on the Pro Trinket. Solder the power and ground wires to the + and - pads on the back of the Pro Trinket.
Plug your battery in again and test to be sure the Neopixel Jewel comes on.
Solder the black wire from the mode button to the G pin on the bottom end of the Pro Trinket. Solder the white wire to pin 3.
Plug your battery in once more and click the mode button to see the Neopixel Jewel change color modes. Tug on all your connections and wiggle things around to make sure all your solder joints are tight.
Getting everything into the handle is a little tricky, but it all fits neatly with a little bit of patience and care. Needle-nose pliers are very helpful here.
Feed the electronics into the handle from the top. Place the on-off switch first. It helps to pull it all the way through while getting the Pro Trinket it place and then press it back so it's flush with the outside of the case. Glue it in place with hot glue.
Once you have the switch in its hole, settle the Pro Trinket at the bottom of the case so you can access the USB port. Glue it in place, being careful not to get any glue inside the USB port.
Slide the battery down next to the Pro Trinket, then set the mode button in place. I found it easiest to tape the button and wires against the inner wall of the handle with gaffer's tape. The handle has a shallow track inside below the switch hole where the wires feed through past the Neopixel Jewel.
Lastly, settle the Neopixel Jewel in place. There's a tiny ledge that will hold it at just the right spot. It's a little tricky to get it settled -- if you're having trouble, be sure the switch wires are settled neatly into the wire channel.
TEST AGAIN AT THIS POINT! Make sure you haven't knocked any wires loose with all that fiddling.
Wrap a few layers of gaffer's tape around the fiber bundle until it fits snugly inside the handle. Gently press it in as far as it will go, being careful not to dislodge the mode button.