Seismic quiescence has attracted attention as a possible precursor to a large earthquake. However, sensitive detection of quiescence requires accurate modeling of normal aftershock activity. We apply the epidemic-type aftershock sequence (ETAS) model that is a natural extension of the modified Omori formula for aftershock decay, allowing further clusters (secondary aftershocks) within an aftershock sequence. The Hector Mine aftershock activity has been normal, relative to the decay predicted by the ETAS model during the 14 months of available data. In contrast, although the aftershock sequence of the 1992 Landers earthquake (M = 7.3), including the 1992 Big Bear earthquake (M = 6.4) and its aftershocks, fits very well to the ETAS up until about 6 months after the main shock, the activity showed clear lowering relative to the modeled rate (relative quiescence) and lasted nearly 7 years, leading up to the Hector Mine earthquake (M = 7.1) in 1999. Specifically, the relative quiescence occurred only in the shallow aftershock activity, down to depths of 5-6 km. The sequence of deeper events showed clear, normal aftershock activity well fitted to the ETAS throughout the whole period. We argue several physical explanations for these results. Among them, we strongly suspect aseismic slips within the Hector Mine rupture source that could inhibit the crustal relaxation process within "shadow zones" of the Coulomb's failure stress change. Furthermore, the aftershock activity of the 1992 Joshua Tree earthquake (M = 6.1) sharply lowered in the same day of the main shock, which can be explained by a similar scenario.