Step 1: Match each movement to its craniovertebral joint. The skull-to-C1 articulation gives nodding, while the C1-to-C2 articulation gives rotation. Side-to-side turning is rotation.
Step 2: The C1-C2 joint is the atlanto-axial joint, a pivot joint in which the dens of the axis acts as the central peg. The ring of the atlas and the transverse ligament spin around this peg.
Step 3: Rotation here swings the face left and right, the classic NO gesture. The atlanto-occipital joint only flexes and extends ($YES$ nodding), and the C2-C3 and C3-C4 joints are typical cervical facet joints that do not generate this dedicated rotation.
Step 4: Turning the head left to right is the function of the atlanto-axial joint.\[\boxed{Atlanto\text{-}axial\ joint}\]