The sensitivity to dark matter signals at neutrino experiments is fundamentally challenged by the neutrino rates, as they leave similar signatures in their detectors. As a way to improve the signal sensitivity, we investigate a dark matter search strategy which utilizes the timing and energy spectra to discriminate dark matter from neutrino signals at low-energy, pulsed-beam neutrino experiments. This strategy was proposed in our companion paper arXiv:1906.10745, which we apply to potential searches at COHERENT, JSNS$^2$, and CCM. These experiments are not only sources of neutrinos but also high intensity sources of photons. The dark matter candidate of interest comes from the relatively prompt decay of a dark sector gauge boson which may replace a Standard-Model photon, so the delayed neutrino events can be suppressed by keeping prompt events only. Furthermore, prompt neutrino events can be rejected by a cut in recoil energy spectra, as their incoming energy is relatively small and bounded from above while dark matter may deposit a sizable energy beyond it. We apply the search strategy of imposing a combination of energy and timing cuts to the existing CsI data of the COHERENT experiment as a concrete example, and report a mild excess beyond known backgrounds. We then investigate the expected sensitivity reaches to dark matter signals in our benchmark experiments.