Abstract The Transiting Exoplanet Survey Satellite (TESS) mission delivers time-series photometry for millions of stars across the sky, offering a probe into stellar astrophysics, including rotation, on a population scale. However, light-curve systematics related to the satellite’s 13.7 day orbit have prevented stellar rotation searches for periods longer than 13 days, putting the majority of stars beyond reach. Machine-learning methods have the ability to identify systematics and recover robust signals, enabling us to recover rotation periods up to 35 days for GK dwarfs and 80 days for M dwarfs. We present a catalog of 7245 rotation periods for cool dwarfs in the Southern Continuous Viewing Zone, estimated using convolutional neural networks. We find evidence for structure in the period distribution consistent with prior Kepler and K2 results, including a gap in 10–20 day cool-star periods thought to arise from a change in stellar spin-down or activity. Using a combination of spectroscopic and gyrochronologic constraints, we fit stellar evolution models to estimate masses and ages for stars with rotation periods. We find strong correlations between the detectability of rotation in TESS and the effective temperature, age, and metallicity of the stars. Finally, we investigate the relationships between rotation and newly obtained spot filling fractions estimated from Apache Point Observatory Galactic Evolution Experiment spectra. Field starspot filling fractions are elevated in the same temperature and period regime where open clusters’ magnetic braking stalls, lending support to an internal shear mechanism that can produce both phenomena.