[Scharfschuetzer]

On the range, you can also try puting opaque tape over the weak eye lense of his shooting glasses. Just one stip over the optical center is usually enough. He can then keep his dominant eye open, yet not really see with it. This will allow him relax and to shoot with his weak eye (strong side) without fighting the instinct to open his dominant eye while he is trying to keep it closed.