We present an analysis of multi-timescale variability in line-of-sight X-ray absorbing gas as a function of optical classification in a large sample of Seyfert AGN to derive the first X-ray statistical constraints for clumpy-torus models. We systematically search for discrete absorption events in the vast archive of RXTE monitoring of dozens of nearby type I and Compton-thin type II AGN. We are sensitive to discrete absorption events due to clouds of full-covering, neutral or mildly ionized gas with columns >~ 10^(22-25) cm^-2 transiting the line of sight. We detect 12 eclipse events in 8 objects, roughly tripling the number previously published from this archive. Peak column densities span ~ 4-26 x 10^22 cm^-2. Event durations span hours to months. The column density profile for an eclipsing cloud in NGC 3783 is doubly spiked, possibly indicating a cloud that is being tidally sheared. We infer the clouds distances from the black hole to span ~0.3 -140 x 10^4 R_g. In seven objects, the clouds distances are commensurate with the outer portions of Broad Line Regions (BLR), or the inner regions of infrared-emitting dusty tori. We discuss implications for cloud distributions in the context of clumpy-torus models. The probability of observing a source undergoing an absorption event, independent of constant absorption due to non-clumpy material, is 0.006(+0.160,-0.003) for type Is and 0.110(+0.461,-0.071) for type IIs.
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