This video shows how to open up a GoPro:
My particular GoPro didn't allow me to solder in the same spot, but every go pro has basically the same shutter button. Under the shutter button are two concentric circles. The middle circle is power, and the outer circle is ground. When you push the button, the circuit is closed.
You can solder a wire to each circle, and run the wires outside of the GoPro. When you touch the wires, the circuit is closed, and the shutter is triggered.
Dimension Engineering makes a great little PWM-activated relay (they call it PicoSwitch):
You attach the hacked GoPro wires into the PicoSwitch, and attach the PicoSwitch servo connection to servo 10 on the PixHawk.
Then go to Mission Planner and navigate to Initial Setup -> Optional Hardware -> Camera Gimbal and make the following settings:
I set channel 7 parameter for camera trigger, and set switch SH on my Taranis to channel 7. SH functions more like a push button than a toggle switch. Works like a charm.