An Unruh-DeWitt detector falling radially into a four-dimensional Schwarzschild black hole, coupled linearly to a massless scalar field that has been prepared in the Hartle-Hawking or Unruh state, has recently been shown to exhibit a local extremum in its transition probability near the black hole horizon [K. K. Ng , ]. We show that a similar phenomenon is present in the transition rate of an Unruh-DeWitt detector falling radially into a spinless Bañados-Teitelboim-Zanelli black hole, with the scalar field prepared in the Hartle-Hawking state. We give extensive numerical results as a function of the detector’s energy gap, the black hole’s mass, and the detector’s drop-off radius. Our results suggest that the effect is robust, motivating a search for a similar effect in other black hole spacetimes, and calling for an explanation of the physical origin of the effect. Published by the American Physical Society 2024