As I understand it, your brain is programmed to favor one eye over the other almost regardless of the acuity in your ocular equipment. From what I’ve observed this impulse is much stronger than handedness. I’ve seen new shooters who were right-handed go through the damndest contortions to get their dominant left eye behind the sights, and vice-versa. (If you’re not sure which is your dominant eye, the test is all over the Internet, so I won’t weary you by describing it here.) And, for what it’s worth, mixed dominance, such as in Page and myself, is more common in women than in men.