#1 How does this affect your putting positively or negatively?
#2 Do people swing right and putt left (or vice versa) as a result of this?
To be honest its not what eye you are dominant with, its what you know and how to use the eye correctly.
I am doing a study on eye dominance and it is becoming obvious that we can train and develop better positions by better focus and how to use our eyes correctly.
I have already seen from many players that getting them to use their eyes properly can change their positions and improve their ability to get into neutral positions that are technically sound.
No clue how how it effects my putting. I am pretty much right eye dominant. I know this because i took a terrain analysis class in college, were you look at two images of the same land area, but there slightly offset, so they get 3D look, its called stereoscopic. But, i had a hard time getting one eye to look at one image and the other eye to look at the other. I was so right eye dominant that it overpowered my vision.
But for me and my putting, i tend to aim about 1 degree left with my current putter.
I am left eye dominant and have tried to putt lefty and righty style.
I feel that if the dominant eye is in the front then I feel more confident with offset style putter like anser /Newport putter with a bit of shaft lean.
When I try to putt left and my dominant eye is at the rear and I prefer the look of a bullseye/seemore FGP center shafted putter and more of a perpendicular shaft at address.
I do lean the shaft forward for some fast breaking putts, but feel confident with that type of putter.
I know there are varying opinions on this topic but this is my own personal experience.