I do look through the peep with my left eye, it's my dominant eye and I also shoot left handed. My guess, just a guess, is you have to shoot dominant eye "handed" to shoot with both eyes open. The peep sight is nothing more than a consistent reference point for where to look. It makes you anchor the same. I can shoot and have shot without a peep, but the string blur in front of my eye bothers me now.

If my people, who are called by my name, will humble themselves and pray and seek my face and turn from their wicked ways, then will I hear from heaven and will forgive their sin and will heal their land. 2 Chronicles 7:14