How do I wire a gazebo
It sounds as if the cable going to the switch just requires a feed. 

I am not sure how you intend to bring power to the gazebo from the main house, but basically you would wire both 12/2 cables to the #12 feed wire and wire it color for color; white to white, black to black, ground to ground. 

The GFI would get wired to the LINE terminals only.

Please comment if you can add any details that might help.