Not to be a smart alec, but we don't walk around all day with one eye closed. lol
Both eyes are open until a target is identified and the rifle lined up for the shot. When my right eye is lined up with the scope or sights, I close my left eye, or use a blinder of some type. It can be an opaque plastic square attached to a pair of shooting glasses, as in my post above, or a bit of tape on the lens as others have posted.
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This is Sheng Lihao of China, who won the Gold at the Paris Olympics in mens 10 meter air rifle. He uses a blinder attached to the rear diopter sight on his rifle.
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This is Yusef Dikec of Turkey, who became a sensation for NOT using shooting glasses or blinders of any type.
Both shooters use what works for them. As a German 10meter coach explained to me, the ability to use both eyes at once is known as binocular accommodation or binocular visual acuity. Every human has a different level of this, and from everything I've been able to gather from some of the best shooting coaches in the World, is that trying to override someones binocular accommodation is usually counterproductive. As I understand it, this is not the eyes themselves, but the brain as it joins the two visual images into one. It is how our individual brain is hard wired from birth.
When I'm out in the field I hunt with both eyes, but I shoot with one eye.