  The TESS space mission is producing superb data for asteroseismology,
eclipsing binary stars, gyrochronology, and other fields of stellar astronomy
where the data are variable light curves. We show that TESS data are excellent
for astrophysical inference from peculiar stars that show variability. The Ap
stars have the strongest magnetic fields of any main-sequence stars. Some have
been shown to have rotation periods of months to centuries. The astrophysical
cause of their slow rotation -- the braking mechanism -- is not known with
certainty. These stars are rare: there are currently about 3 dozen with known
periods. The magnetic Ap stars have long-lived spots that allow precise
determination of their rotation periods. We show that most Ap stars with TESS
data that show no low-frequency variability must have rotation periods longer
than a TESS sector of 27 d. We find 60 Ap stars in the southern ecliptic
hemisphere TESS data with no rotational variability, of which at most a few can
be pole-on, and six likely have nearly aligned magnetic and rotation axes. Of
the other 54, 31 were previously known to have long rotation periods or low
projected equatorial velocities, which proves our technique; 23 are new
discoveries. These are prime targets for long-term magnetic studies. We also
find that 22 per cent of long-period Ap stars are roAp stars, versus only 3 per
cent of the other Ap stars studied with TESS sector 1 and 2 data. This work
demonstrates astrophysical inference from nonvariable stars -- "something for
nothing".
