I don't really think it's so much as of a matter if it CAN be done, but from what I can tell, the binary trigger makers are both doing so with the addition that the selector can be manipulated so as to be able to fire only a single time.
If you were to try to do this with the scorpion, it would be a dedicated all the time, fire on the pull and the release.
Also, I'm pretty certain that a new selector would need to be produced.
I'll add this here:
https://www.youtube.com/watch?v=_4pxAS9mQCY
How so? There's room in there for a second disconnector. You could mount it on the left side and cut the spacer and have two. The tricky part is getting the selector to pick which one you want to use. But I think you could simply hit the shaft with a welder and then shape it into a ramp that would push down on a tail that is common in a lot of firearms.
As stated in his video - the BAFTE didn't like his gen 1 kit. The gen 2 solved this by running two disconnectors. It definitely shed some light on the hammer follow of a single modified disconnector as well. Where they are modified to touch and go, and holding the trigger at the exact right spot allows the hammer to sneak by. The third gen used a live disconnector that changed orientation based on the pull or release. Sounds fancy. No idea how that's happening.
I think the selector shaft could easily be welded on and shaped to create a ramp to actuate tails on the disconnectors. I already explained how to get a third position on the selector. So, in theory you could have primary and secondary disconnectors that allowed normal function, and then pull and release function. The only thing I can't work out in my head is how much fiddling it would take with the trigger hooks and hammer to make the sides operate independently, but still overlap enough to catch the hammer so there was no hammer follow window.
I know it can be done. Simply shimming the (unmodified) disconnector creates the binary function and once it's in the teeny tiny window where this happens, I didn't observe any hammer follow. That said, I wasn't trying to prove a case, or even create a binary trigger. Simply see how much slop needed to come out, or if I could get the disconnector to stay away from the back of the hammer to eliminate it's spring stacking into the trigger pull without grinding it back. It did however prove a 5 thou window exists where the gun will release the hammer on pull and release. And that was without modifying any parts.