Here's what the headlight looks like on front of my bike (w/ headlight guard and before I replaced my homemade gutter guard, oil cooler guard w/ the TT one for the 1150) and my R1150GS Beak Transplant:
And, here's what the original wiring looked like for the TT Dual H4 Sockets (of course everything is upside down here because I just flipped it down on the front of my bike.
The TT Dual Headlight has a coupler just like you'll get with the Eastern Beaver relay harness that couple's to the 11GS's original H4 bulb socket. The TT's blue and green colored wires w/ their blue and black H4 bulb sockets are removed entirely. My new harness appears much more robust than the TT wiring anyway. The brown wires that connects to the GS's original parking light wire remains and the TT kit splits to run a parking light bulb to each side. Of course these are different bulbs than stock (which I had just bought an LED for). Eventually I'll find the correct LED to go in each to replace.