A model previously shown to provide physically meaningful interpretation of a wide range of polymer-penetrant relaxation-induced non-Fickian (including case II) sorption kinetics, is used here as a basis for a deeper understanding of fundamental case II kinetic features. In particular, we report and discuss model calculation results on the dependence of penetration velocity v, and of important characteristics of the concentration profile, on the main material parameters which characterize the system. The latter include the polymer relaxation rate constant relative to the diffusion constant, the parameters measuring the magnitude of the (exponential) concentration dependence of these constants, and the sorptive capacity of unrelaxed, relative to relaxed, polymer. A precisely defined relaxation lifetime is evaluated analytically and shown to provide a simple single-parameter link between penetration velocity behavior and relaxation kinetics. In the same vein, a quantitative measure of the steepness of the sharp penetration front, also amenable to analytical evaluation, is proposed and its application illustrated.