Results of further calculations on the dynamic coupling between the lower Blu and Elu electronic states of benzene via a single e2g mode are presented. In part I we gave the 'pseudo-cylindrical' solutions that result when the leading coupling term, linear in the nuclear displacements, is considered (cylindrical Born-Oppenheimer potential). Here we investigate the effect of (1) the next higher terms in the expansion of the coupling hamiltonian for the free molecule (hexagonal Born-Oppenheimer potential); (2) a crystal field anisotropy. From the scanty data on the coupling constants available a priori it would follow that the refinement introduced by (1) is small for benzene. On the contrary, the effect of even a small crystal field anisotropy is predicted to be appreciable.The results of the calculations are analysed by comparison with experimental data on the benzene crystal at low temperature. A consistent interpretation of both magnetic resonance results and the triplet~ singlet absorption spectrum is obtained.