  The neutrinos from a Type II supernova provide perhaps our best opportunity
to probe cosmologically interesting muon and/or tauon neutrino masses. This is
because matter enhanced neutrino oscillations can lead to an anomalously hot
nu_e spectrum, and thus to enhanced charged current cross sections in
terrestrial detectors. Two recently proposed supernova neutrino observatories,
OMNIS and LAND, will detect neutrons spalled from target nuclei by neutral and
charged current neutrino interactions. As this signal is not flavor specific,
it is not immediately clear whether a convincing neutrino oscillation signal
can be extracted from such experiments. To address this issue we examine the
responses of a series of possible light and heavy mass targets, 9Be, 23Na,
35Cl, and 208Pb. We find that strategies for detecting oscillations which use
only neutron count rates are problematic at best, even if cross sections are
determined by ancillary experiments. Plausible uncertainties in supernova
neutrino spectra tend to obscure rate enhancements due to oscillations.
However, in the case of 208Pb, a signal emerges that is largely flavor specific
and extraordinarily sensitive to the nu_e temperature, the emission of two
neutrons. This signal and its flavor specificity are associated with the
strength and location of the first-forbidden responses for neutral and charge
current reactions, aspects of the 208Pb neutrino cross section that have not
been discussed previously. Hadronic spin transfer experiments might be helpful
in confirming some of the nuclear structure physics underlying our conclusions.
