Quick update. Here is the finished thing:

It lasts for about 10 hours continuous display on a 1200mAh battery.

In the end I opted for having the battery on the back of the chain so it sits on the back of the wearer's neck. This keeps the pendant itself shorter. Wires are threaded through the chain - I used small gauge speaker wire - one strand is gold, the other silver so I can tell which is positive and which negative.

I programmed the pendant itself to respond to taps and double taps. Single taps turn it in for short periods of time - strong movements have the same effect. Double taps turn it on permanently or off.

For a long time I couldn't figure out how to attach the pendant to the chain. In the end I used transparent heat-shrink tubing to completely enclose the electronics and HV and then made a coil of brass wire that the tube could be slipped into and the chain attached. Here is a photo before the pendant was slipped into the brass coil: