I got one of these at a flea market. Runs off one cell. Has some sort of transformer/relay device all rolled into one. This thing REALLY hurts when you use it, I wouldn't recommend it for the weak hearted. It is not a quick one time zap like a cigarrete lighter(which by the way is 100x less painful), but a continous shock until you release the button. I'm not even sure it's legal.
So... on with the explanation.
The end of the coil unit you can see has a metal disc and an inner nipple, the two of which are insulated from eachother. Pushing the button compresses the battery spring until the inner part makes contact with the battery.
When that main coil is energized, I think it acts as a magnet and pulls the slab of metal on that thin strip, which disconnects the coil I guess, at which point it is free to return and reconnect the coil.
The main housing of the pen is metal, and the very tip of the push button is also metal, which is unsulated from the rest of the housing. The tip of the button connects directly to the negative end of the battery.
There is a little strip that starts near the base of the coil unit, it used to be longer, but was broken short by accident. This gets wedged against the main pen body when the whole thing is put together.
Internally, I'm still a bit confused on which parts of the coil unit connect to eachother and in what way exactly.