Perceptual flicker when rotating my face
I'm guessing that you are experiencing the interplay of two mechanisms: When you start to turn your head, the "vestibulo-ocular reflex" tries to hold the visual scene steady by counteracting your head movement. But as you continue to turn your head (apparently at about 30 deg. intervals), a "saccade" kicks in to restore your gaze to a point straight in front of your face.

A similar effect can be observed when the visual scene moves, as when you look out a train window, but in this case, rather than the vestibulo-ocular reflex, it would be "smooth pursuit eye movement" that tries to hold the visual scene steady. (Wikipedia has good articles for all three of the quoted terms.)

An interesting way to check this hypothesis would be to videotape your face as you perform the experiment and observe your eye movements in the video. I'm looking forward to a YouTube posting...