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 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.
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.