As Earth's precession is caused by the differential solar, etc., attraction to its 'spare tire', then does the rate go to ~zero at the equinoxes and ~twice the average at the solstices? (preferred answer: yes :-)
Or is there some 'carry-over' 'precessional momentum' that keeps the annual rate more constant? (preferred answer: no :-)
The contribution to the precession from the sun does depend on the time of year (basically because tidal forces have a azimuthal symmetry around the line connecting the bodies but no polar symmetry), but there is also a contribution of similar magnitude from the moon, so the overall effect has a more complicated time dependence and only rarely drops to zero.
The inertia in the system is the angular momentum of the planet which will have a constant direction if there is no torque. Nor should you be imagining the tidal torque just disappearing, it rises and falls smoothly.
