I shot rifles for years with a RH hold and left eye by putting on high mounts and using an odd cheek weld with my neck bent way over to the right, my cheek almost horizontal over the stock and my nose on the far side of the stock. I could get my left eye lined up in the scope, but it wasn't in the center of the field of vision. And worse, it was NOT the way you want to hold any rifle with any substantial recoil, unless you want a bloodied nose. When I learned to shoot a bow, it was impossible to cross over, so I learned to shoot a bow and arrow lefty. And several years back, I had a broken hand and wore a cast for several weeks. Spent that time learning to shoot pistols left handed.
No, the only proper way to shoot is with both eyes open and the sights in line with the center of the field of vision in your dominant eye. Your neck should be relaxed and you shouldn't close or need to squint one eye. Otherwise, you get muscular tension, an odd position that makes it much harder to be steady, and a loss of visual acuity. No matter how odd it feels, the only good solution, ultimately, is to put the rifle on the side of your dominant eye.
