Originally Posted by Bugguts
I have the same problem and got roundly criticized for it in my handgun class when I first started shooting because it eliminates your peripheral vision and in the case of multiple assailants, that can be a problem. I still don't shoot with both eyes open since I kind of squint my left eye but they do have these dots that you can put on your shooting glasses to cover the right or left eye that I am thinking about trying out. They are called Shooters Magic Eye Dots. Here's a link.
Stan from TASC just put some masking tape on my glasses to achieve the same thing. I still shoot cross-eye dominant though, really difficult to overcome.