  We present a study of the variation timescales of the chromospheric activity
indicator H$\alpha$ on a sample of 13 fully-convective, active mid-to-late M
stars with masses between 0.1--0.3 solar masses. Our goal was to determine the
dominant variability timescale and, by inference, a possible mechanism
responsible for the variation. We gathered 10 or more high-resolution spectra
each of 10 stars using the TRES spectrograph at times chosen to span all phases
of stellar rotation, as determined from photometric data from the MEarth
Observatories. All stars varied in their H$\alpha$ emission. For 9 of these
stars, we found no correlation between H$\alpha$ and rotational phase,
indicating that constant emission from fixed magnetic structures, such as
starspots and plage, are unlikely to be the dominant source of H$\alpha$
emission variability. In contrast, one star, G 7-34, shows a clear relationship
between H$\alpha$ and stellar rotational phase. Intriguingly, we found that
this star is a member of the AB Doradus moving group and hence has the young
age of 149 Myr. High-cadence spectroscopic observations of three additional
stars revealed that they are variable on timescales ranging from 20--45
minutes, which we posit may be due to flaring behavior. For one star, GJ 1111,
simultaneous TESS photometry and spectroscopic monitoring show an increase in
H$\alpha$ emission with increased photometric brightness. We conclude that
low-energy flares are able to produce variation in H$\alpha$ on the timescales
we observe and thus may be the dominant source of H$\alpha$ variability on
active fully-convective M dwarfs.
