If your skull line across the eyes matches the aim of the putterface, so your neck points parallel to the top edge of the putter, and your gaze is straight out of the face, and your head turns on a stable axis, your line of sight will trace a straight line from the putter sweetspot straight along the ground the same as the putter face is aimed. If the putter face is aimed at the target, the line of sight of the unchanging straight gaze will arrive at the target, with the target fitting in the aim spot of the dominant eye.
It sounds like your head-neck axis is shifting during the turn so that the top of your head alters slightly away from the target (backwards). If you can keep your neck aimed straight the same as the top of the putter from heel to toe while turning towards the target, this will not occur.
You may not be squaring the skull line correctly, but may instead be setting up with the head a little "open" -- an arrow thru the two ears is not parallel to the line of aim, but is aimed a little to the outside (right). If you are using the proim glasses, with the slot between the two lines matching the string or rope above the aim line, this should not be the case.
Another thing that may happen is that the eyes change direction in the eye sockets during the head turn. he eyeballs are seated in a pocket of fatty tissue so that they will move about effortlessly without being noticed. If you are right-eye dominant, try closing the left eye once the skull is squared above the putter, and extending the index finger of your left hand as if pointing right across the bridge of your nose, with the tip of the finger just stopping at your right eye's pupil (about 1 inch of finger rightward from the bridge of the nose). Then turn the head so that the finger appears to glide in a straight line and wait to see what appears at the tip of the finger once the turn gets as far as the target. This will keep your skull line / head-neck axis from shifting the top of the head backwards and will also keep the eyeball from changing the way it points out of the face.
In general, there is an arch at the top of the nose for most people as seen by the dominant eye while the other eye is closed. The pupil is not as high as this arch, but a little below it, which you can see in a mirror. If you close the left eye and turn the head targetward and wait to see what shows up just below this arch, that's pretty much keeping the gaze straight. I use this reference often instead of using the left index finger.
Try that and let me know.
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