  We use time-domain optical spectroscopy to distinguish between broad emission
lines powered by accreting black holes (BHs) or stellar processes (i.e.,
supernovae) for 16 galaxies identified as AGN candidates by Reines \etal
(2013). Our study is primarily focused on those objects with narrow
emission-line ratios dominated by star formation. Based on follow-up spectra
taken with the Magellan Echellette Spectrograph (MagE), the Dual Imaging
Spectrograph, and the Ohio State Multi-Object Spectrograph, we find that the
broad H$\alpha$ emission has faded or was ambiguous for all of the star-forming
objects (14/16) over baselines ranging from 5 to 14 years. For the two objects
in our follow-up sample with narrow-line AGN signatures (RGG 9 and RGG 119), we
find persistent broad H$\alpha$ emission consistent with an AGN origin.
Additionally, we use our MagE observations to measure stellar velocity
dispersions for 15 objects in the Reines et al. (2013) sample, all with
narrow-line ratios indicating the presence of an AGN. Stellar masses range from
$\sim5\times10^{8}$ to $3\times10^{9}$~\msun, and we measure $\sigma_{\ast}$
ranging from $28-71~{\rm km~s^{-1}}$. These $\sigma_{\ast}$ correspond to some
of the lowest-mass galaxies with optical signatures of AGN activity. We show
that RGG 119, the one object which has both a measured $\sigma_{\ast}$ and
persistent broad H$\alpha$ emission, falls near the extrapolation of the $\rm
M_{BH}-\sigma_{\star}$ relation to the low-mass end.
