A comprehensive dynamic analysis of the dielectric relaxation-time data across a broad temperature range for both isotropic and nematic phases has been conducted on the CBO3O.Py liquid crystal dimer, the shorter chain-length compound within the highly nonsymmetric pyrene-based series of liquid crystal dimers (CBOnO.Py, with n ranging from 3 to 11). It was known from another previous study that in the nematic phase, three different relaxation processes contribute to the complex dielectric permittivity depending on the orientation of the alignment axis with respect to the probing electric field direction. The temperature-derivative analysis of the relaxation-time data using different analytic functions reveals that the critical-like description, through the dynamic scaling model, best portrays the relaxation-time data in the nematic phase as the system approaches the glass transition. A single glass transition temperature is obtained which is consistent with thermal stimulated depolarization currents experimental determinations published elsewhere. From temperature-dependent steepness index m(T), the activation-critical model is also considered as a more general analytic function from which the dynamic scaling model is a terminal approximation. Additionally, the critical-like parametrization provides insight into obtaining a universal description of the temperature-dependent steepness index m(T), for all liquid crystal compounds belonging to symmetry-selected glass formers, such as rodlike liquid crystal monomers.