It seems kind of wierd that you can shoot with either eye...either hand I can figure, but the dominant eye is usually pretty "fixed."
When I shot IPSC a lot of matches had "Weak Hand Only" stages, and kind of similarly I always seemed to shoot slightly better with my left hand, but they were always close, either 7 or 10 yards max, and usually involved a string of 6 with both, a reload, then the transfer to the weak hand, then one handed with the weak hand only, in anywhere from 8 to 12 seconds depending on the match, I would have my right hand holding onto my shirt front with a death grip after I kind of "swept" the gun into the other hand, so I didn't wiggle with it waving around with nothing to do
. Several times I had ROs question me if I was actually left handed. Many times the second 6 were better than the first 6!
I would cant the .45 though and use my right eye, and since the .45 recoils up and to the right, it was easy to get back on target if I shot them left to right...the muzzle moved on it's own to the next target with the recoil and all I had to do was let it drop down a little and the sights were right on the center of the next target.
But I am a little strange too...I'm right handed/right eyed in shooting, writing, throwing, BUT I have always batted left handed, shot left handed when I played Hockey, and Golf left handed.