The Two Higgs Doublet Model (2HDM) is an extension of the Standard Model (SM) of particle physics in which one additional complex scalar doublet is introduced into the theory. The extension to a non-minimal Higgs sector produces several new features beyond the SM. One such feature is that the 2HDM can have non-trivial vacuum topology predicting 3 distinct domain wall solutions from the breaking of 3 accidental symmetries at the electroweak scale. We present numerical kink solutions for all three cases. In particular, we discuss the dependence of features in these kink solutions on the physical parameters of the model, i.e. Higgs masses and mixing angles. We also present numerical simulations of the evolution of domain wall networks in these models for certain parameter sets consistent with current experimental constraints. We discuss the scaling behaviour of these networks and connections to the interaction of kinks in these models. These results provide a view into the phenomenology of 2HDM domain walls as a cosmological probe of extended Higgs sectors and their potential to provide complementary constraints to particle physics experiments.