A combined experimental and theoretical study of transition matrix elements of the $6p{}^{2}{P}_{j}\ensuremath{\rightarrow}8s{}^{2}{S}_{1/2}$ transition in atomic Cs is reported. Measurements of the polarization-dependent two-photon excitation spectrum associated with the transition were made in an $\ensuremath{\approx}200{\mathrm{cm}}^{\ensuremath{-}1}$ range on the low-frequency side of the $6s{}^{2}{S}_{1/2}\ensuremath{\rightarrow}6p{}^{2}{P}_{3/2}$ resonance. The measurements depend parametrically on the relative transition matrix elements, but also are sensitive to far-off-resonance $6s{}^{2}{S}_{1/2}\ensuremath{\rightarrow}\mathrm{np}{}^{2}{P}_{j}\ensuremath{\rightarrow}8s{}^{2}{S}_{1/2}$ transitions. In addition, as the measured quantities are ratios of polarization-dependent intensities at a single-excitation frequency, they are quite insensitive to a variety of common-mode systematic effects; matrix-element ratios may then be determined to high accuracy. In the past, the matrix-element dependence has yielded a generalized sum rule, the value of which is dependent on sums of relative two-photon transition matrix elements. In the present case, best available determinations from other experiments are combined with theoretical matrix elements to extract the ratio of transition matrix elements for the $6p{}^{2}{P}_{j}\ensuremath{\rightarrow}8s{}^{2}{S}_{1/2}(j=1/2,3/2)$ transition. The resulting experimental value of 1.423(2) is in excellent agreement with the theoretical value, calculated using a relativistic all-order method, of 1.425(2).