Eye dominance can be a factor, but it doesn't have to be. Basically, there are two ways of aiming: binocular, with chin centered over the cue (no eye dominance); dominant eye aiming. Both work fine.
Allison Fisher has always been one of pool's best shot makers, and she aims with the binocular method. What one must be aware of, if you use both eyes centered in binocular aiming, you must aim from the cueball to the object ball and ignore where the cue shaft points.
Dominant eye aiming permits you to sight down the shaft, through the cueball, to the object ball. Everything lines up and looks "right", like sighting a rifle.
You think there is a problem with opposite eye dominance? I think the opposite might be true. Willy Mosconi, Mike Sigel and Jim Rempe are all opposite eye shooters. Can you think of three better shotmakers? (Someone wrote Earl was opposite eye dominant. Wrong! That's so far from correct it made me smile.)
Learning to shoot dominant eye if you've been aiming binocular, can be a challenge. I believe it's worth the effort. At least it has been for me. I can relate my experiences and hope it helps you.
I played for over 30 years as a binocular aimer. But I was never a really good long shot shooter. So I decided I'd try dominant eye shooting.
Well, the first problem I encountered was I couldn't make a ball! I had a huge problem trying to aim at all. Finally, I simply closed my non-dominant eye (my left), and tried that. It seemed to work. After spending nearly a whole day at it, I learned to sight with both eyes open, with my dominant eye over the cue. But that didn't solve all. I could make a straight in shot, but had a hellava hard time with cuts.
I had a conversation with the superb teacher, Chan Whit. He suggested I move the cue slightly from directly under my DE toward my nose. He said to move until the shaft no longer appeared to aim at the cueball, then come back. That helped me a lot, and seemed to be my way of aiming. However, I have found that gradually the shaft moved directly under my dominant eye, where I keep it now. I don't know if that is a common path, or something idiocyncratic to my style.
What I started to realize after addressing the aiming conundrum, was aiming was the easy part. Delivering the cue straight is a far more vexing problem for most players. I believe more shots are missed because of improper cue delivery than aiming.
So, I'm not sure, if your goal is to improve your shotmaking, if you can adjust your aiming without taking stock of your stroke mechanics, stance, grip and alignment. It's all a package. If one thing is off, you miss.
Anyway, around this time, I got Max Eberly's Power Pool. I believe Max has put the best instruction on stance and alignment available on DVD. Production values are kind of amateurish, but the information and the quality of coaching is in a class by itself. I highly recommend it.
Armed with Max's stance guidelines, I sought to correct a stance issue that has plagued me since I started: I was too over the cue and my shooting elbow was tucked inside, well off plane. Funny, too, I always thought my stance was pretty good. I had a 14.1 high run of 83, with tons of 50+ runs. So I was a decent player, but compensating for errors.
The dominant eye aiming was comparatively easy to learn. Re-doing one's mechanics, after decades of doing it wrong, was not so easy. But I knew, on the occassions when I would do it right, how powerful it would be to do it right all the time.
And so, for nearly six months, I devoted every lunch hour to training. I'd shoot from the spot to the center diamond, being sure the cueball rebounded straight. This establishes if you can hit the cueball in the center. But my favorite drill is a long straight shot, diagonally across the table. Nothing gives you as much feedback. For me, if I developed a pattern of missing left, I knew my elbow was creeping back to its former place of comfort. This was a very persistent problem and required constant vigilence. But I can say, after hitting this shot a few thousand times, I can usually deliver the cueball dead on, no spin, no cut. When I can do it on a dead stop shot, repeatedly, I do it with draw and follow, and vary the force from soft to as hard as I can shoot it.
Was it worth the effort? God, yes! I wish I did this years ago. The keys are commitment and patience. But the net result is, I shoot better now at 62 than I ever have. Much better!
I can't say enough about Max's DVD. You might also look at Joe Tucker's Third Eye DVD and gadget; it helped some. Also, Gene Albrect's Perfect Aim DVD will help answer a lot of questions. Ironically, I contacted Gene about the time I had solved my own aiming issues. But in conversation with him, I realized he teaches what I learned through trial and error. So don't do like me, reinventing the wheel. Gene's info is excellent.