  M dwarfs remain active over longer timescales than their Sunlike
counterparts, with potentially devastating implications for the atmospheres of
their planets. However, the age at which fully-convective M dwarfs transition
from active and rapidly rotating to quiescent and slowly rotating is poorly
understood, as these stars remain rapidly rotating in the oldest clusters that
are near enough for a large sample of low-mass M dwarfs to be studied. To
constrain the spindown of these low-mass stars, we measure photometric rotation
periods for field M dwarfs in wide binary systems, primarily using TESS and
MEarth. Our analysis includes M-M pairs, which are coeval but of unknown age,
as well as M dwarfs with white dwarf or Sunlike primaries, for which we can
estimate ages using techniques like white dwarf cooling curves, gyrochronology,
and lithium abundance. We find that the epoch of spindown is strongly dependent
on mass. Fully-convective M dwarfs initially spin down slowly, with the
population of 0.2--0.3M$_\odot$ rapid rotators evolving from $P_{\rm rot} < 2$
days at 600 Myr to $2 < P_{\rm rot} < 10$ days at 1--3 Gyr before rapidly
spinning down to long rotation periods at older ages. However, we also identify
some variability in the spindown of fully-convective M dwarfs, with a small
number of stars having substantially spun down by 600 Myr. These observations
are consistent with models of magnetic morphology-driven spindown, where
angular momentum loss is initially inefficient until changes in the magnetic
field allow spindown to progress rapidly.
