I just purchased a outdoor pavilion that came with an electrical package. It includes a #12 two wire plus a ground wire going into an electrical box for the on and off switch to run the fan and another #12 two wire plus ground wire going into a GFI outlet box. The GFI outlet should run constant while the switch should run when turned on. My questions is how to correctly wire this. The power will be running off the GFI outlet.
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.