RZ Psc is a young Sun-like star, long associated with the UXor class of variable stars, which is partially or wholly dimmed by dust clumps several times each year. The system has a bright and variable infrared excess, which has been interpreted as evidence that the dimming events are the passage of asteroidal fragments in front of the host star. Here, we present a decade of optical photometry of RZ Psc and take a critical look at the asteroid belt interpretation. We show that the distribution of light curve gradients is non-uniform for deep events, which we interpret as possible evidence for an asteroidal fragment-like clump structure. However, the clumps are very likely seen above a high optical depth midplane, so the disc's bulk clumpiness is not revealed. While circumstantial evidence suggests an asteroid belt is more plausible than a gas-rich transition disc, the evolutionary status remains uncertain. We suggest that the rarity of Sun-like stars showing disc-related variability may arise because (i) any accretion streams are transparent and/or (ii) turbulence above the inner rim is normally shadowed by a flared outer disc.G.M.K. is supported by the Royal Society as a Royal Society University Research Fellow. J.E.R. is supported as a Future Faculty Leaders Fellow at the Harvard-Smithsonian Center for Astrophysics. M.C.W. acknowledges support from the European Union through ERC grant no. 279973. Early work on KELT-North was supported by NASA grant no. NNG04GO70G
