I'm a right-eyed, right handed shooter, and I noticed the same thing. Without knowing it, I would turn my head in to the extent that my right eye was blocked from the target, maybe by my nose, so I was "aiming" with my left eye some of the time, which of course threw my shots off as you describe. I found out about this when I had a cataract operation and went around for a while without any left lens in my eyeglasses, which made it real obvious when I switched from right to left eye. Now that both eyes have been fixed, I try to be careful not to turn my head in to the extent that my right eye is blocked.