New sets of young M dwarfs with complex, sharp-peaked, and strictly periodic photometric modulations have recently been discovered with Kepler/K2 and TESS data. All of these targets are part of young star-forming associations. Suggested explanations range from accretion of dust disks to co-rotating clouds of material to stellar spots getting periodically occulted by spin-orbit-misaligned dust disks. Here we provide a comprehensive overview of all aspects of these hypotheses, and add more observational constraints in an effort to understand these objects with photometry from TESS and the SPECULOOS Southern Observatory (SSO). We scrutinize the hypotheses from three different angles: (1) we investigate the occurrence rates of these scenarios through existing young star catalogs; (2) we study the longevity of these features using over one year of combined photometry from TESS and SSO; and (3) we probe the expected color dependency with multi-color photometry from SSO. In this process, we also revisit the stellar parameters accounting for activity effects, study stellar flares as activity indicators over year-long time scales, and develop toy models to imitate typical morphologies. We identify which parts of the hypotheses hold true or are challenged by these new observations. So far, none of the hypotheses stand out as a definite answer, and each come with limitations. While the mystery of these complex rotators remains, we here add valuable observational pieces to the puzzle for all studies going forward.
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