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 active galactic nuclei ( 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 Rossi X-ray timing Explorer 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 \ga 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 \sim 4 - 26 \times 10 ^ { 22 } cm ^ { -2 } , i.e. , there are no full-covering Compton-thick events in our sample . 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 \sim 0.3 - 140 \times 10 ^ { 4 } R _ { g } . In seven objects , the clouds ’ distances are commensurate with the outer portions of Broad Line Regions ( BLR ) , or outside the BLR by factors up to \sim 10 ( the inner regions of infrared-emitting dusty tori ) . We discuss implications for cloud distributions in the context of clumpy-torus models . Eight monitored type II AGN show X-ray absorption that is consistent with being constant over timescales from 0.6 to 8.4 yr . This can either be explained by a homogeneous medium , or by X-ray-absorbing clouds that each have N _ { H } \ll 10 ^ { 22 } cm ^ { -2 } . 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 .