In order to make this necklace as user-friendly as possible, we'll add a battery charger right into the design. That way you can just plug your necklace in to your computer with a USB Micro cable whenever he gets dim. (This also makes him into a wonderful gift for people who are not as tech-savvy as you are).
Solder three header pins into the charging backpack.
Take a utility knife and break the trace between the two connected pins next to the header. This will enable you to add an on/off switch to the necklace.
Solder a long (1.5 - 2 foot) black silicone 26awg wire to each of these two pins. These will later become your necklace cords so make them long enough to reach around your neck when the board is hanging at pendant height.
Solder the 3 header pins into the Trinket Pro using the BUS, G, and BAT+ pins next to the USB port. Trim off any extra header sticking out on the back side.
Solder a power, ground and data wire to the Neopixel Jewel as shown. It works best to have the wires come in from the LED side and solder on the back side.
Solid core wires work best here! You want them to hold their shape when you bend them and stranded wires are tougher to work with in this case.
Putting it All Together
Make a little sandwich of all your electronics with the LEDs on top, the battery next, then the Trinket Pro and the charging backpack on the bottom. The battery pack itself then acts as a non-conductive insulator between the metal pentant and the Pro Trinket board.
Bend the Neopixel Jewel wires around and line them up with their corresponding pins on the Trinket Pro. Cut them to length while you're holding the battery in place.
Pull the battery out of the way and solder the Neopixel Jewel to the board, being sure to leave space to put the battery back when you're done.
Jewel PWR -> Trinket JST +
Wrap the battery in electrical tape to avoid any shorts between components and help with strain relief.
Plug in your JST connector and slip all the components into place in their neat little stack. Wind the wire from the battery around so it's hidden, or you can shorten the wires and splice them back together if you prefer. Set them in your pendant and admire your handiwork.