The seminal concept of a persistent spin texture (PST) characterized by a momentum-independent spin orientation in a spin-orbit coupled system was introduced through the Rashba-Dresselhaus model in Phys. Rev. Lett. 90, 146801 (2003). By considering the combined Rashba and Dresselhaus spin-orbit coupling (SOC) interactions, the study predicted the emergence of a PST under very highly restrictive conditions of equal SOC strength. The present work introduces two low-energy effective Hamiltonians H_MKM1 and H_MKM2, incorporating Weyl- and Dresselhaus SOC interaction terms. Remarkably, these Hamiltonians yield a persistent spin texture when the constituent SOC strengths are equal. In contrast, for unequal SOC strengths, these models accurately reproduce the recently identified partial PST (P-M2) observed in the OsSi crystal near the high-symmetry PST point located at the Brillouin-zone boundary [Nat Commun 16, 7999 (2025)]. By benchmarking a wide range of PST models against first-principles calculations for nonsymmorphic and noncentrosymmetric two-dimensional (2D) and bulk materials, this work uncovers a diverse range of spin-texture behaviours and highlights their distinct characteristics across different dimensionalities. This study identifies a few-layer AgI (110) as a promising 2D semiconductor platform for realizing persistent spin texture. Through rigorous theoretical analysis, this work further reveals that the PST phase can be destabilized by the application of a finite out-of-plane electric field, highlighting the sensitivity of the spin texture to the external electric-field perturbation.