  Images of supermassive black holes produced using very long baseline
interferometry provide a pathway to directly observing effects of a highly
curved spacetime, such as a bright ``photon ring'' that arises from strongly
lensed emission. In addition, the emission near supermassive black holes is
highly variable, with bright high-energy flares regularly observed. We
demonstrate that intrinsic variability can introduce prominent associated
changes in the relative brightness of the photon ring. We analyze both
semianalytic toy models and GRMHD simulations with magnetic flux eruption
events, showing that they each exhibit a characteristic ``loop'' in the space
of relative photon ring brightness versus total flux density. For black holes
viewed at high inclination, the relative photon ring brightness can change by
an order of magnitude, even with variations in total flux density that are
comparatively mild. We show that gravitational lensing, Doppler boosting, and
magnetic field structure all significantly affect this feature, and we discuss
the prospects for observing it in observations of M87* and Sgr A* with the
next-generation Event Horizon Telescope.
