  We examine the commonly explored beyond-standard-model physics scenario of
secret neutrino forces, and point out a model prediction that appears to have
been overlooked: the generation of unique flavor-changing effects in
experiments featuring decay-at-rest (DAR) neutrino sources. These flavor
changes occur because the decay that drives neutrino and antineutrino
production, $\mu^{+}\rightarrow e^+ +\bar{\nu}_{\mu}+\nu_{e}$, is unique in
producing two neutrinos in the final state. Any non-flavor-universal force
between the emerging neutrinos would thus induce a new oscillation phase as
they escape from each-other's potential wells, an effect which is largely
absent in experiments that primarily rely on meson decay-in-flight and nuclear
decay. We calculate the magnitude of the associated observable and compare it
to the anomalous neutrino flavor transformation seen by the LSND experiment,
finding a wide but constrained allowed parameter space. We also evaluate
existing limits from other experiments, and the testability of this new effect
at the future DAR programs JSNS$^2$ and OscSNS.
