  Fully convective M dwarfs typically remain rapidly rotating and magnetically
active for billions of years, followed by an abrupt and mass-dependent
transition to slow rotation and quiescence. A robust understanding of this
process is complicated by difficulties in estimating M-dwarf ages and potential
dependencies on other variables such as birth environment or metallicity. To
isolate the effect of mass, we consider M dwarfs in wide binaries. We identify
67 widely separated, fully convective (0.08-0.35M$_\odot$) M-dwarf binary
systems using Gaia and measure the H$\alpha$ feature for each component. We
classify the pairs into three categories: systems where both components are
active, systems where both are inactive, and candidate transition systems,
where one component is active and the other inactive. We gather
higher-resolution spectra of the candidate transition systems to verify that
their behavior does not result from an unresolved third component, yielding one
new triple with surprising activity levels. Neglecting this triple, we find 22
active, 36 inactive, and 8 transition pairs. Our results are consistent with
the epoch of spindown for these binaries being primarily determined by mass,
with mild second-order effects; we place a 1$\sigma$ upper limit of 0.5Gyr or
25% on the dispersion in the mass-dependent spindown relation. Our findings
suggest that the large dispersion in spindown epoch previously observed for
field stars of a given mass may stem from differences in birth environment, in
addition to modest intrinsic stochasticity. We also see evidence that the wide
binary population is dispersed over time due to dynamical processing.
