We have conducted an extensive X-ray spectral variability study of a sample of 20 Compton-thin type II galaxies using broad band spectra from XMM-Newton, Chandra, and Suzaku. The aim is to study the variability of the neutral intrinsic X-ray obscuration along the line of sight and investigate the properties and location of the dominant component of the X-ray-obscuring gas. The observations are sensitive to absorption columns of $N_{rm H} sim 10^{20.5-24} {rm cm^{-2}}$ of fully- and partially-covering neutral and/or lowly-ionized gas on timescales spanning days to well over a decade. We detected variability in the column density of the full-covering absorber in 7/20 sources, on timescales of months-years, indicating a component of compact-scale X-ray-obscuring gas lying along the line of sight of each of these objects. Our results imply that torus models incorporating clouds or overdense regions should account for line of sight column densities as low as $sim$ a few $times 10^{21}$ cm$^{-2}$. However, 13/20 sources yielded no detection of significant variability in the full-covering obscurer, with upper limits to ${Delta}N_{rm H}$ spanning $10^{21-23}$ cm$^{-2}$. The dominant absorbing media in these systems could be distant, such as kpc-scale dusty structures associated with the host galaxy, or a homogeneous medium along the line of sight. Thus, we find that overall, strong variability in full-covering obscurers is not highly prevalent in Compton-thin type IIs, at least for our sample, in contrast to previous results in the literature. Finally, 11/20 sources required a partial-covering, obscuring component in all or some of their observations, consistent with clumpy near-Compton-thick compact-scale gas.
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