I shoot with both eyes open no matter which side. I am left handed, but was told at age 7 to shoot right handed, as most guns are built that way and life would be simpler. I have a vague recollection of some struggle to use my right eye, but trained out of it and can now (I am 49) switch from side to side with no conscious effort. If it is difficult for you to use your non-dominant eye if that is not your more talented hand, try this. put a piece of scotch tape on the lens of your shooting glasses for your dominant eye, and allow your brain to work with the remaining available image. Avoid closing one eye when shooting, as the muscle work involved will compress and somewhat change focus of the open eye. For practice, spend some glassing time with your spotting scope, keeping both eyes open and switching from side to side every few minutes. You can train your brain to process the images if you put in the time. When you do get behind the rifle, use the tape on glasses trick to finish the process. Which ever way you ultimately decide to go, you can make it work. Some people can train the "dumb" hand easier, others can train the "dumb" eye easier. You will find which option is best for you.