There are many in the scientific community (the large majority) who believe there is no such thing as a "dominant eye", except for people with visual problems in a single eye.
I know for a fact that eye dominance exists, because I can feel it very well. I'm right-eye dominant, and I "prefer" seeing something with that one if I close an eye. Even better, it must be hard-wired somewhere in my brain, because my right eye sees much less well than my left, yet I always go for that one if I want to eyeball the straightness of something.
If you were a person who believes that "dominant eye" is an urban myth; do you think such a person could get anything from the Perfect Aim Method???
Without revealing the method, the eye dominance thing is just a small part of it. It just determines from which side you approach the visual "sweet spot" at which you're supposed to see the shot perfectly.
When I talked to Gene on the phone, I realized that I was already doing what he explains in his method. I do it instinctively, so in a sense it's my own version of the method. The only difference with the real Perfect Aim method is that I approach the aforementioned sweet spot from any side, so I basically throw Gene's eye dominance element out the window.
The main idea of the method is to feel it "click" in your head when your aiming is just right. It's like a light that goes green when you're all set. The entire Perfect Aim method is just a set of formal instructions to get you to feel when you're visually all set to shoot. Once you've felt the visual sweet spot enough times, your brain will want to find it again automatically and instinctively: at that point, you can forget the method altogether, you won't need it anymore, it'll have done its job.
So yes, you can use the Perfect Aim method without any concept of eye dominance, but you may have trouble following Gene's instructions if you ignore it, because Gene uses it to describe what you should do to approach the sweet spot. If, despite doing it in reverse, you can feel when your eyes are at the right spot, then no problem.