  The Tucana-Horologium Association (Tuc-Hor) is a 40 Myr old moving group in
the southern sky. In this work, we measure the rotation periods of 313 Tuc-Hor
objects with TESS light curves derived from TESS full frame images and
membership lists driven by Gaia EDR3 kinematics and known youth indicators. We
recover a period for 81.4% of the sample and report 255 rotaion periods for
Tuc-Hor objects. From these objects we identify 11 candidate binaries based on
multiple periodic signals or outlier Gaia DR2 and EDR3 re-normalised unit
weight error (RUWE) values. We also identify three new complex rotators
(rapidly rotating M dwarf objects with intricate light curve morphology) within
our sample. Along with the six previously known complex rotators that belong to
Tuc-Hor, we compare their light curve morphology between TESS Cycle 1 and Cycle
3 and find they change substantially. Furthermore, we provide context for the
entire Tuc-Hor rotation sample by describing the rotation period distributions
alongside other youth indicators such as H{\alpha} and Li equivalent width, as
well as near ultra-violet and X ray flux. We find that measuring rotation
periods with TESS to be a fast and effective means to confirm members in young
moving groups.
