I've always shot with both eyes open, especially with a scope. It makes my target acquisition very fast because both eyes always look to the same spot. It will take a little time to develope and get use to, but once you get use to it you won't even realize you're doing it. Your dominant eye is already use to your sight picture, now you just have to get use to letting your other eye see the target too, while not actually focusing with it.
"Why is is called Common Sense when it seems so few actually possess it?"
Guns only have two enemies: Rust and Politicians.