The well-known switch of the polarization state of a Zeeman laser's emission into a single longitudinal mode as the cavity length is detuned is re-examined using a model that goes beyond third-order Lamb theory by retaining equations for the dynamics of the material variables for a J = 1 to J = 0 transition. For certain parameter values, the output of the laser as described by this model is predominantly two orthogonally polarized modes with different optical frequencies, as in third-order Lamb theories studied previously, but the more complicated field-material dynamics and near-threshold time-dependent solutions present in this model also give rise to more complicated pulsations and polarization dynamics as the cavity is detuned. Also as in third-order Lamb theories, in this model the preference (stability) for circularly or linearly polarized single mode emission depends on the ratio of the decay rates of the magnetic dipole and the electric quadrupole of the J = 1 level. For conditions in which the cross-saturation preference is for linearly polarized emission and there are weak linear anisotropies, the switching of the polarization state as the cavity is detuned has a range of overlap of the two polarization states (and corresponding time dependent dynamics) rather than the abrupt switching and hysteresis or polarization rotation more commonly found in simpler models. The detuning range for the overlap is sensitively dependent on the strength of the cross-saturation coupling. While there is similar exchange of relative dominance of two polarized modes when there is the combination of weak circular polarization anisotropies and cross-saturation preference for linearly polarized emission, the overlap region remains large, and it is relatively independent of the relaxation rate of the coherence between the upper levels. By comparing these results with experimental behavior found in a xenon laser which operates on a J = 3 → J = 2 transition we can estimate the effective parameters of the model suitable for describing certain features of this experimental situation, even though the xenon laser is known to have its preference for linearly polarized emission arise directly in the field-matter interaction rather than solely from relaxation rate differences as it does in the model considered here.