The HD 80606 system, which consists of a stellar binary with a transiting high-eccentricity (e=0.933) Jupiter-sized companion planet, is a textbook example of Kozai migration. It is one of the best-characterized planetary systems to date, with high-amplitude Doppler velocities, secondary eclipse observations, and a precise stellar obliquity measurement. However, the rotational properties of HD 80606b remain enigmatic. Spitzer observations have suggested that the rotation rate of HD 80606b is much slower than the pseudosynchronous prediction, indicating a need for further observational constraints and improved dynamical models in the high-eccentricity regime. We revisit the HD 80606 system with new datasets from TESS and Gaia to place improved constraints upon the dynamics of this cornerstone system.