Is it possible for a planetary body to have a secondary axis of rotation? For example let's say there's an Earth-like body that is spinning with its North Pole facing the Sun. Imagine that the North Pole is always facing the Sun, in a somewhat tidally locked position. Is this even possible? Is it possible for the actual axis of rotation to change over time in a predictable and stable way?
I'm aware that the axial tilt can vary and oscillate with time. I guess what I'm asking is, is it possible for the axial tilt itself to be tidally locked to another astronomical body? Is it possible for the axial tilt to rotate on its own axis independent of perturbations from other bodies?
Good answers will provide me with a yes or no, as well as providing me examples of possible celestial bodies that already show this feature. Provide links or pictures for bonus points.
The relation to worldbuilding is that in my story, I'm trying to have the main planet actually be a moon of a large gas giant, yet be livable, have seasons, and have equatorial and polar differences in temperature. My original idea was using the L1 Lagrangian point of the gas giant so that it maintains a pretty consistent distance from the sun, but this point cannot be stabilized in a natural way. (See my previous question here)