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We present an analysis of the core linear polarization properties of 387 parsec-scale active galactic nuclei (AGNs) jets. Using 15 GHz VLBA data, we revisit the conclusions of the first paper in this series with multiepoch measurements and more detailed analysis of a larger AGN sample that spans a broader range of synchrotron peak frequencies. Each AGN has been observed for at least five epochs between 1996 and 2017. We find that BL Lac objects have core electric vector position angles (EVPAs) that tend toward alignment with the local jet direction; compared to flat spectrum radio quasars, their EVPAs are also less variable over time. The AGN cores that are most fractionally polarized and least variable in polarization have EVPAs that are closely aligned with the local jet direction; they also have low variability in EVPA. These results support the popular model of a standing transverse shock at the base of the jet that collimates the jet magnetic field perpendicular to the jet direction, increasing the fractional polarization and leading to greater polarization stability over time. High-synchrotron-peaked BL Lac objects form a low luminosity, low fractional polarization population. The five narrow line Seyfert 1 galaxies in our sample have low fractional polarization and large EVPA-jet misalignments. Although AGNs detected at γ-rays are thought to be more Doppler boosted than nondetected AGNs, we find no significant differences in fractional polarization based on detection by Fermi-LAT; the γ-loud AGNs are, however, more variable in core EVPAs. [ABSTRACT FROM AUTHOR]