High-resolution photoelectron spectra of RgS(-) (Rg = Ne, Ar, and Kr) were obtained using slow electron velocity-map imaging (SEVI). The SEVI spectra reveal well-resolved vibrational transitions between multiple spin-orbit states of RgS(-) and RgS, both of which are open-shell species. Detailed assignments are made by comparison with theoretical simulations based on high level ab initio calculations and a atoms-in-molecule model that accounts for spin-orbit coupling in the anion and neutral. Several RgS(-) and RgS vibrational frequencies and excited-state term energies are accurately determined from the analysis of the experimental spectra and are found to be in excellent agreement with the calculated values.