This is pretty interesting stuff, everybody's got their own way of doing it. I'm right handed, right eye dominant, and have always shot both eyes open. Interestingly, I don't focus on the sights at all, because of the double image thing. Instead, I seem to focus on the target while looking through the sights. On harder shots (40 yards +) I do tend to close my left eye, but not always. It works for me.
<<Later edit>> I was thinking about this post and had to go get a gun and look. Sure enough, I get the double sight image with both eyes open, but I guess I'm so used to it that I never notice. I just always use the clearer sights on the left. Easier to deal with double sights than double target. Maybe I need to practice more...