The moon's circle of illumination runs parallel with the Earth's and at right angles to the Sun -
https://solarsystem.nasa.gov/resourc...=planets_earth
Rather than use information against an exceptionally unpleasant notion of a pivoting circle of illumination, astronomers would use that orbital function to discern the motion of the North and South poles as they move across the fully illuminated face of the Earth and turn parallel to the orbital plane.