I just noticed another interesting idea that is somewhat controversial. To keep it unbiased try this exercise first.
Slowly touch your nose with your index finger.
Wait for it
What did you find? I found that my brain prefers to use an arc when moving the hand. Next time I tried moving my index finger in a straight line to my nose. I noticed that my hand wavered along the line. I accomplished the task with accuracy but there was a noticeable difference between the two ways of touching my nose. The arc is (to me) much smoother and the preferred method. I can be equally accurate with either method but the arc simply feels better or more natural.
Perhaps the brain prefers this type of integral calculus for making the necessary adjustment during targeting. It can be forced to work a pump action but a pendulum or arc type swinging motion is "preferred" by my brain.
Well I guess you can see the controversy there. Apparently the pendulum swing is preferred by the brain. Oh my, what are all those snooker players going to say
Then too I have an old brain so maybe the pump is better for some
And finally, touching your nose has nothing to do with pool playing, yeah, right.
Interesting insight, I would apply it in another way. Since we aren't looking at our arm motion while shooting, it's not as relevant to me. But while aiming, quite a few players come into the cue ball from one side or the other and not in a direct motion. Perhaps that's also how the pivot based aiming systems help us segment the shots into categories related to the relationship of the balls and the geometry of the shot/table and then sweep in from left to right or right to left, allowing our brain to zero in on the precise angle in a way that's feels so locked in...
Not saying you need to use an aiming system to gain a benefit from this, many of the pros have this movement while shooting. I just think that along with the initial systematic alignment, which changes based on the relative sizes of the balls and the relationship to the pocket, we get to within a few degrees of the shot and maybe our visual process is able to zero in even further and automatically makes minute adjustments on the way in from there.
Scott