I used to be left eye dominant right hand shooter, then I retrained myself. Unless you are handicapped and your shooting side eye is impaired, I believe anyone can retrain themselves.

I took a pair of shooting glasses and sandpapered the left eye lens to a blur. Not being able to see clearly through that eye anymore, my brain natrually seeks the clearer image.

We tried this out on our hunter ed students and were probably about 80% successful. I think it is better to blur the vision in the off eye rather than blank it as the lack of light and subsequent dilation of the pupil in that eye poses other undesirable effects.

On a tangent, we discovered that many of the kids who were nearsighted, such as my daughter, could retrain their eyes to focus at depth by wearing a cover over their eyes that had a pinhole in it. For some reason looking through that pinhole their vision goes to near perfect again.

Go figure.