The discovery of the top quark, the most massive elementary particle yet known, has given us a distinct window into investigating the physics of the Standard Model and beyond. With a plethora of top quarks to be produced in the high luminosity era of the LHC, the exploration of its rare decays holds great promise in revealing potential new physics phenomena. We consider higher-dimensional operators contributing to flavour-changing-neutral-current top decays in the SMEFT and its extension by a light singlet species of spin 0, 1/2, or 1, and exhibit that the HL-LHC (and other future colliders) may observe many exotic top decays in a variety of channels. Light singlets which primarily talk to the SM through such a top interaction may also lead to distinctive long-lived particle signals. Searching for such long-lived particles in top-quark decays has the additional advantage that the SM decay of the other top quark in the same event provides a natural trigger.