Richard, there is a center tapped ground on that light coil. That's why he sees 1.1Ξ© from each wire to frame with nothing else connected.
If it it required an external ground both of those measurements would read as an open circuit.
Per the wiring diagram already linked in this thread, the green wire powers the brake light (via the brake lever switches; they should be normally closed type); the black wire powers the head light, tail light, and horn.
Regarding the bike running with the switch off, the contacts may be corroded / dirty. The stop switch grounds the ignition coil, and if there's a poor connection there it'll just run. A little isopropyl alcohol on an old toothbrush will clean 'em right up.
When you put 6V on the brake / tail light, how did you connect it? The bulb should have two terminals on the bottom, and a ground terminal around the base.
If you connected 6V across the two terminals on the bottom, then it makes sense that both filaments lit up, as they are effectively in series. You should be able to connect 6V from either terminal to frame ground and light up one filament at a time.
Assuming there are no wiring errors on the bike, that is. :)