Last update for me.
The 60s interfere with the electrical system of the 2008 K1200GT under any configuration--by pass box, autoswitch trigger with relay, and separate circuit with a relay and manual switch all induce the same interference. It must be something the lights emit, or the unshielded wiring? I just don't know and I never did get a response from the vendor.
By the way Clearwater lights guarantees their lights will work with the K12GT. They are much more $$, but if you have a K12GT and want LED's this may be a better option.