  We report on the discovery of broad Balmer absorption lines variability in
the QSO SDSS J125942.80+121312.6, based on the optical and near-infrared
spectra taken from the SDSS-I, SDSS-III Baryon Oscillation Spectroscopic Survey
(BOSS), and TripleSpec observations over a timescale of 5.8 years in the QSO's
rest-frame. The blueshifted absorption profile of H$\beta$ shows a variation of
more than 5$\sigma$ at a high velocity portion ($>3000\ \mathrm{km\ s}^{-1}$)
of the trough. We perform a detailed analysis for the physical conditions of
the absorber using Balmer lines as well as metastable He I and optical Fe II
absorptions ($\lambda 4233$ from b$^4$P$_{5/2}$ level and $\lambda 5169$ from
a$^6$S$_{5/2}$) at the same velocity. These Fe II lines are identified in the
QSO spectra for the first time. According to the photoionization simulations,
we estimate a gas density of $n(\mathrm{H})\approx 10^{9.1}\ \mathrm{cm}^{-3}$
and a column density of $N_{\mathrm{col}}(\mathrm{H})\approx 10^{23}\
\mathrm{cm}^{-2}$ for the BOSS data, but the model fails to predict the
variations of ionic column densities between the SDSS and BOSS observations if
changes in ionizing flux are assumed. We thus propose transverse motion of the
absorbing gas being the cause of the observed broad Balmer absorption line
variability. In fact, we find that the changes in covering factors of the
absorber can well-reproduce all of the observed variations. The absorber is
estimated $\sim 0.94$ pc away from the central engine, which is where the
outflow likely experiences deceleration due to the collision with the
surrounding medium. This scheme is consistent with the argument that LoBAL QSOs
may represent the transition from obscured star-forming galaxies to classic
QSOs.
