What rotation does the eye use?

In the shortest rotation from left to right, w tilts as much as the gaze direction.

The rotation with no tilt of w, is longer.

During saccades, w tilts halfway between the shortest and the longer. This eye follows Listing's law; the half angle rule,

Thus during saccades, the eye does not make the shortest possible rotation between the initial and final gaze directions.

To see what each eye would see change your viewpoint to inside each eye.

Notice that when your viewpoint is inside the eye that follows Listing's law (the one with the blue axis), horizontal grid lines are not parallel with the eye's horizontal.

The horizontal line appears to turn clockwise when the eye looks right and counterclockwise when it looks left.