I started out mostly squinting my left eye, and using my right, and that worked pretty well.
Then I read the various reasons why using both eyes is theoretically better, so I switched over.
Shooting right-handed, or with both hands on the weapon, it actually works very well.
I find that I shoot to the right, though, when I try using both eyes if shooting left-handed (weak hand for me). Left-handed, I still have to nearly shut one eye, but I've found that it's the right one that gets mostly closed. If I line up my left hand and left eye, I hit dead center.
Not sure if this is correctable (IE, if there's a way to train to use both eyes, when there is such a noticeable difference, for weak-hand shooting).