We present the continuation of J. Maj\'ar [Phys. Rev. D 80, 104028 (2009)] to solve the instantaneous spin precession equations for the spin-orbit, spin-spin, and quadrupole-monopole contributions. In this paper we present the solution of the quadrupole-monopole contributions to the precession equations. For eccentric orbits we use the true anomaly parametrization, and for circular orbits our results are given explicitly in terms of the time variable. We also give a detailed analysis of the different effects of the spin interactions, and investigate which of these are relevant in the present case. We work in the framework of the post-Newtonian expansion.