looking at that diagram, the whole pups are always in parallel with each other since they both are always kind of attached to the volume pot at the 'north finish' wire. In the 3rd position, you get a normal les paul style 3 way toggle middle position setup.
If someone can confirm... In position one, the bridge pup 'north finish' and 'south finish' wires are joined, while on the neck, 'south finish' becomes grounded along with the 'south start' and shield, and the 'north start' and 'north finish' wires get joined, which I guess in effect turns the pup off, even though it is still connected to the volume pot.