Breathe for Touch

At address when looking along the line at the hole turn the head targetward while breathing in through the nose casually and time the completion of a not-especially-deep inspiration to coincide with the arrival of the face and gaze looking dead at the target. This is the lifting open of the bellows that expand the chest a little over a specific time. THEN JUST RELAX TO ALLOW THE BREATH TO ESCAPE SMOOTHLY as the head turns back along the line from target to ball. Nothing forced. Pause looking at the ball a moment for the gaze for the gaze and sense of balance to clarify after the head stops moving. Then start your backstroke in coordination with the same nasal in-breathing going back to the top of the backstroke, so that the chest expansion and timing of the breath establishes the backstroke length instinctively. From the top of the backstroke relax (release the bellows) to transpire as the breath escapes smoothly thru the nose.
Practiced a few times you will be amazed how much it helps the pace of your putts.