Summarizeing: SJCam didn't tell you exactly what you want to know. You're unhappy about that. If I still had all the money I spent on products that left me in the same situation, I would be flying around in my personal jet. Oh wait, there are some unclear points in the Gulfstream pilot's manual and they didn't mention I have to populate the panel myself. Life is like that. I agree that the documentation needs a complete re-write, and there should be a mic/power cable. I doubt the manual will be rewritten, but a DIY mic/power cable is possible. It only needs someone to do the job, and share how they did it, or to start selling them.
Addrd: there's a YouTube video about making a cable. Unfortunately, there may be a problem with knowing if all SJ7's use the same connector. It would be a big help if someone would resolve the matter: yes or no.