We apply the weirddetector, a non-parametric signal detection algorithm based on phase dispersion minimization, in a search for low duty-cycle periodic signals in the Transiting Exoplanet Survey Satellite (TESS) photometry. Our approach, in contrast to commonly used model-based approaches specifically for flagging transits, eclipsing binaries, or other similarly periodic events, makes minimal assumptions about the shape of a periodic signal, with the goal of finding 'weird' signals of unexpected or arbitrary shape. In total, 248301 TESS sources from the first-year Southern sky survey are run through the weirddetector, of which we manually inspect the top 21500 for periodicity. To minimize false-positives, we here only report on the upper decile in terms of signal score, a sample for which we obtain 97% recall of TESS eclipsing binaries and 62% of the TOIs. In our sample, we find 377 previously unreported periodic signals, for which we make a first-pass assignment that 26 are ultra-short periods (<0.3d), 313 are likely eclipsing binaries, 28 appear planet-like, and 10 are miscellaneous signals.