We present the multi-epoch analysis of 13 variable, nearby (z<0.1), Compton-thin (22<logN_H<24) active galactic nuclei (AGN) selected from the 105-month BAT catalog. Analyzing all available archival soft and hard X-ray observations, we investigate the line-of-sight hydrogen column density (N_H) variability on timescales ranging from a few days to approximately 20 years. Each source is analyzed by simultaneously modeling the data with three physical torus models, providing tight constraints on torus properties, including the covering factor, the cloud dispersion, and the torus average hydrogen column density (N_H,av). For each epoch, we measure the N_H and categorize the source as `N_H Variable', `Non-variable in N_H', or `Undetermined' based on the degree of variability. Our final sample includes 27 variable, Compton-thin AGN after implementing another 14 AGN analyzed in our previous work. We find that all sources require either flux or N_H variability. We classify 37% of them as `N_H Variable', 44% as `Non-variable in N_H', and 19% as `Undetermined'. Noticeably, there is no discernible difference between geometrical and intrinsic properties among the three variability classes, suggesting no intrinsic differences between the N_H-variable and non-variable sources. We measure the median variation in N_H between any observation pair of the same source to be 25% with respect to the lowest N_H measure in the pair. Furthermore, 48% of the analyzed sources require the inclusion of a Compton-thick reflector in the spectral fitting. Among these, the 30% exhibits recorded 22 GHz water megamaser emission, suggesting a potential shared nature between the two structures.