First, are you sure you are right eye dominant? Focus at a spot on the wall or something. Hold your thumb out at arms length with both eyes open and align the tip of your thumb with the spot. Close one eye at a time. When your thumb moves you just closed your dominant eye.
As for one or two, use both, it is the only way to go. If you are shooting in a defensive/combat/ action sport manner try using more of an isosceles upper body index if you don't and rotate your head so that your dominant eye is closer to the gun, straight behind the sights. For example, I am left handed and eyed. If I rotate my head about 15deg. to the right it puts myleft eye directly behind the gun and occludes my right eye just enough so that my brain sees my left eye picture only rather than two bullseyes. another option is to put a piece of scotch tape on your glasses over your non-dominant eye. I usually don't have to do much of either, if I get the two bullseye syndrome I just blink my non-dominant eye once and I then regain the right picture. My one weakness is rifle scopes, if I look through one with my right eye while keeping my left eye open I see black in the scope.
The advantages of two eye are more visual input of what the gun is doing, depth perception for movement and ranging, as well as peripheral input for moving and finding things to shoot. Even for static paper punching, closing one eye will fatigue the muscles in the open eye causing lack of focus and fatigue. One last thing is to trust your inputs. Close range I see the target very clearly and vaguely see a gun. Farther out I see a pretty front sight and a vague target. Your eye can focus on one thing at a time. Best to try not to focus at all, let your face relax, recieve peripheral/secondary vision inputs and just shoot. Experience will tell you what you need to see and how much. The cool thing about shooting fast(which I obviously like) is first you have to be accurate before fast to succeed. After that,you go through stages where what used to look fast to you looks slow. I think that the limiting factor in shooting accurately quickly is how fast we have taught our brain to recognize visual inputs.