You'll probably never see the GS in the act if they're doing it at night (which I'm willing to lay a buck on - no more). Separate them and see what happens. Keep in mind that if the fins are damaged often some more dieback will occur, but usually you can see discoloration and then it frays off. Unfortunately, this method of detective work will take some time to "prove" my hypothesis as it takes a while to grow those fins (although I have "rescued" bettas with almost no fins left and gotten them back to their original splendor).
I finally gave up trying to keep bettas with anything else (though I know some do quite successfully). Besides the M/F betta tank with lots of plants and cover, my favorite setup was a 10 gallon with an undergravel filter (to ensure good water flow on both sides) with a home made plexiglass divider. You could do the same with any tank with two air driven sponge filters too - I know some keep bettas with no filter but i wanted the movement as I used only 1 heater and I'm into keeping bettas warm with a good cover to keep the top layer of air which they breathe warm too.
Anyhow, there was a male on each side and they displayed to each other off and on and were happy as clams. Really cool to watch.
) i was gonna add neons but I dont have any luck with them. Lol 
