  We test for an anisotropy in the mass of arriving cosmic-ray primaries
associated with the galactic plane. The sensitivity to primary mass is obtained
through the depth of shower maximum, $X_{\rm max}$, extracted from hybrid
events measured over a 14-year period at the Pierre Auger Observatory. The sky
is split into distinct on- and off-plane regions using the galactic latitude of
each arriving cosmic ray to form two distributions of $X_{\rm max}$, which are
compared using an Anderson-Darling 2-samples test. A scan over roughly half of
the data is used to select a lower threshold energy of $10^{18.7}\,$eV and a
galactic latitude splitting at $|b| = 30^\circ$, which are set as a
prescription for the remaining data. With these thresholds, the distribution of
$X_{\rm max}$ from the on-plane region is found to have a $9.1 \pm
1.6^{+2.1}_{-2.2}\,$g$\,$cm$^-2$ shallower mean and a
$5.9\pm2.1^{+3.5}_{-2.5}\,$g$\,$cm$^-2$ narrower width than that of the
off-plane region and is observed in all telescope sites independently. These
differences indicate that the mean mass of primary particles arriving from the
on-plane region is greater than that of those from the off-plane region. Monte
Carlo studies yield a $5.9\times10^{-6}$ random chance probability for the
result in the independent data, lowering to a $6.0\times10^{-7}$
post-penalization random chance probability when the scanned data is included.
Accounting for systematic uncertainties leads to an indication for anisotropy
in mass composition above $10^{18.7}\,$eV with a $3.3\,\sigma$ significance.
Furthermore, the result has been newly tested using additional FD data
recovered from the selection process. This test independently disfavors the on-
and off-plane regions being uniform in composition at the $2.2\,\sigma$ level,
which is in good agreement with the expected sensitivity of the dataset used
for this test.
