I am also right handed and left eye dominate, fortunately for me my father (60 years ago) caught it at an early age and made me shoot left handed with a "you'll thank me later remark"....
But I am Cross Dominate which makes shooting with both eyes open, both rifle and shotgun difficult. Knowing that shooting with both eyes open was important he put tape on my glasses to cover the pupil on my right eye (left for you) when my head is on the stock.. You quickly get use to the thumb nail size piece of tape never seeing it when your head is up or when on the stock
My 3 trips to Africa 2 Ele Cows, 3 Buff and other assorted game have been with Iron sights and both eyes open
Toss me a PM if you want further info
But I am Cross Dominate which makes shooting with both eyes open, both rifle and shotgun difficult. Knowing that shooting with both eyes open was important he put tape on my glasses to cover the pupil on my right eye (left for you) when my head is on the stock.. You quickly get use to the thumb nail size piece of tape never seeing it when your head is up or when on the stock
My 3 trips to Africa 2 Ele Cows, 3 Buff and other assorted game have been with Iron sights and both eyes open
Toss me a PM if you want further info