So:
-If you connect a power socket to it, then you can get power for heated clothes and you can charge the battery.
-If you connect heated grips to it, then you get heat in the grips.
-If you connect it to an alarm, then the alarm works fine.
Please let me ask you this:
-How is that possible? ??
You need to know where the other end are, or where the electrisity are going or coming from!
When I got the small BMW-computer (shows speed and time and things) I could NOT connect it to the first contact I saw - I had to find the right/correct one.
And that did NOT look like the contact on your picture.
I have the manual for fitting the auxillary power socket for my Scarver, and as far as I can see, there are two wires in that system - there are three in your mystery contact.
Scarver and GS are not the same, but I do believe you need only two wires for the power socket.
I still believe hazard flashes are the best suggestion, and that is because your bike does NOT have it now (it means you can add one if you want) and because there are three wires in you mystery contact
and in the hazard flash system/button.
Please let me know when you find out!

Liv.