Context. Gamma Doradus (hereafter γ Dor) stars are gravity-mode pulsators whose periods carry information about their internal structure. These periods are especially sensitive to the internal rotation and chemical mixing, two processes that are currently not well constrained in the theory of stellar evolution. Aims. We aim to identify the pulsation modes and deduce the internal rotation and buoyancy travel time for 106 γ Dor stars observed by the Transiting Exoplanet Survey Satellite (TESS) mission in its southern continuous viewing zone (hereafter S-CVZ). We rely on 140 previously detected period-spacing patterns, that is, series of (near-)consecutive pulsation mode periods. Methods. We used the asymptotic expression to compute gravity-mode frequencies for ranges of the rotation rate and buoyancy travel time that cover the physical range in γ Dor stars. Those frequencies were fitted to the observed period-spacing patterns by minimising a custom cost function. The effects of rotation were evaluated using the traditional approximation of rotation, using the stellar pulsation code GYRE. Results. We obtained the pulsation mode identification, internal rotation, and buoyancy travel time for 60 TESS γ Dor stars. For the remaining 46 targets, the detected patterns were either too short or contained too many missing modes for unambiguous mode identification, and longer light curves are required. For the successfully analysed stars, we found that period-spacing patterns from 1-yr-long TESS light curves can constrain the internal rotation and buoyancy travel time to a precision of 0.03 d^-1 and 400 s, respectively, which is about half as precise as literature results based on 4-yr-long Kepler light curves of γ Dor stars.