  We (re)consider the sensitivity of past (LSND) and future (JSNS^2) beam dump
neutrino experiments to two models of MeV-scale pseudo-Dirac dark matter. Both
LSND and JSNS^2 are close (24-30 m) to intense sources of light neutral mesons
which may decay to dark matter via interactions involving a light mediator or
dipole operators. The dark matter can then scatter or decay inside of the
nearby detector. We show that the higher beam energy of JSNS^2 and resulting
$\eta$ production can improve on the reach of LSND for light-mediator models
with dark matter masses greater than $m_\pi/2$. Further, we find that both
existing LSND and future JSNS^2 measurements can severely constrain the viable
parameter space for a recently-proposed model of dipole dark matter which could
explain the 3.5 keV excess reported in observations of stacked galaxy clusters
and the Galactic Center.
