For SD purposes, keeping both eyes open gives one a better view of their surroundings.
First, you have to know which of your eyes is dominant.
For those who don't know, extend both arms in front of you. With palms outward, extend index fingers and thumbs, touching mating digits to form a pyramid. At the peak of the pyramid, focus on an object ten feet or more away behind it. One at a time, close each eye. Whichever eye the object stayed in line with the peak is the dominant eye.
Next is to practice with looking down the handgun sights with both eyes open and maybe turning your head ever so slightly for the dominant eye to be more in line with sights. At the range, it may take a bit more concentration for a while to get use to the sight picture. But for SD you may be only shooting 20 ft. or less.