When you look in the headlight, do you see a small 5w "parking light" bulb. I'm not sure if the American GZs have them, like the European version. If there's no small bulb, then the connector is likely for that. Manufacturers seem to like a standard wiring loom that contains the wiring for anything required around the world. Like, our bikes don't have the marker lights in the front indicator housings, but the wiring's there.
