Sturmey Archer Dynohub

I know it's neither CCM nor Canadian but hopefully someone will know:

I recently aquired a 1950's Robin Hood 3 speed with the Sturmey Archer Dynohub on the front wheel. The wiring is in pretty poor shape and is broken at one of the dynohub terminals, so only one wire to from the hub to the headlight is connected. When the wheel is turning, the headlight shines bright like it should, but the tail light does not work. I checked the bulb and its fine. 

So here are my questions:

1. How is there a complete circuit to the headlight when one wire is not attached? Does it ground somewhere on the frame?

2. How can I get the tail light working?

3. What sort of wire can be used to rewire the system, it looks simillar to speaker wire

If anyone can help I'd greatly appreciate it!