Topological insulators (TIs) have garnered significant interest in condensed matter physics and materials science due to their unique properties. Recently, Half-Heusler compounds have been predicted to exhibit topological insulator behavior based on electronic structure. We conducted a study on potential alternatives for optoelectronic, photorefractive, and photovoltaic devices. Using density-functional-theory (DFT) calculations, a systematic comparison of the structural, electronic, and optical properties of LiAuS and NaAuS is performed. The geometrically optimized structures of cubic LiAuS and NaAuS were compared with theoretical values. The electronic band structure revealed a non-trivial zero band gap at the G-point, and the influence of different orbitals on the conduction band (CB) and valence band (VB) was analyzed. The optical properties including absorption, reflectivity, index of refraction, extinction coefficient, conductivity, and dielectric function were examined over the energy spectrum ranging from 0 to 30 eV. LiAuS displays a notable absorption peak at 7.95 eV, whereas NaAuS exhibits a peak at 6.79 eV. The reflectivity peak, on the other hand, is higher at 19.79 eV and 8.29 eV for LiAuS, and at 6.74 eV for NaAuS. The reflective indices for LiAuS and NaAuS are determined to be 3.5 and 7.03, respectively. It is observed that LiAuS and NaAuS possess elevated optical conductivity at 6.26 eV and 6.14 eV, respectively. The conductivities of LiAuS and NaAuS in terms of their visual properties have been claimed to be 8.0(1/fs) and 6.84(1/fs), individually. In view of its high dielectric constant, LiAuS exhibits significant absorption peaks at 0.91 eV, 4.63 eV, and 13.63 eV, whereas NaAuS displays peaks at 0.07 eV, 4.45 eV, and 13.12 eV. Owing to their optical characteristics, LiAuS and NaAuS possess the potential for implementation in photorefractive and optoelectronic devices.