Flembo, being wrong handed to your dominant eye is more common than you might think. Too, there are those of us who have "sometimes" cross dominance
That being if I sight both eyes open with open sights, I see a "weak" set of sights and target not strong but weak. As I am about to shoot, all of a sudden, I am looking at the left side of the gun, as my left eye has taken over.
If I maintain looking it might bounce back in a few seconds or not. Closing, then reopening both eyes will have me back to my normal right eye dominance. WEIRD. Early on, when a kid, I learned to shoot and sight with my left eye closed. If shooting running game with scope both eyes open. If shooting "flying" game, both eyes open only looking at the 'target'.
Having to close my left eye has not hurt my shooting very much, I feel.