Here are the last steps in constructing an AV plug that will fit inside the GoPro waterproof housing-
All the parts are cut down to leave room for the soldered connections, don't cut them too short or the plug will be weak and floppy. The plastic insulation has NO heat tolerance at all! be very careful if you have to solder near it, even high temp hot glue will distort it if you are not careful and conservative with the heat!
I use a small amount of hot glue to insulate anything that needs it and to help hold everything together as I put the parts back together, this is a bit fussy, you may prefer to use something that gives you more time, like epoxy or liquid tape. Just be very careful to not make a mess on the outside of the plug, also be careful not to mar any of the contact surfaces of the poles during all this taking apart and putting together!
Now just use some hot glue or epoxy etc. to create a strain relief that holds everything down as flat as possible. Hot glue is nice here because it can be shaped or removed very easily.
This plug is very fragile! Never pull it out of the camera by the wires, simply wedge a fingernail under the metal shoulder and pull it out.
Now drill a small hole in the back of the case, feed your wires through and terminate them with the connector of your choice, seal the penetration and go fly!
If you don't need the audio signal this project can be done much easier, as the video and ground are very simple to solder, that audio wire is a bit of a bitch to attach without adding too much bulk and making it impossible to slip everything back together. I don't recommend omitting any of the parts even if they are not attached to a wire, the plug gets really weak and the female jack in the camera likes to have the original form of the plug. If the plug comes apart inside the camera it's not that big of a deal to take the camera apart and push the pieces out of the jack, but obviously you'll be happier to avoid this.