  Modern-day accelerator neutrino facilities are excellent venues for searches
for new-physics particles. Many distinct new-physics models predict overlapping
signatures and phenomenology in these experiments. In this work, we advocate
for the adoption of simplified frameworks when studying these types of
new-physics signatures, which are characterized by a small number of primary
variables, including particle masses, lifetimes, and production and decay
modes/rates that most directly control signal event rates and kinematics. In
particular, taking the example of long-lived particles that decay inside a
neutrino detector as a test case, we study formulate and study simplified
frameworks in the context of light scalars/fermions produced in kaon decays
which then decay into final states containing an electron-positron pair. We
show that using these simplified frameworks can allow for individual
experimental analyses to be applicable to a wide variety of specific model
scenarios. As a side benefit, we demonstrate that using this approach can allow
for the T2K collaboration, by reinterpreting its search for Heavy Neutral
Leptons, to be capable of setting world-leading limits on the Higgs-Portal
Scalar model. Furthermore, we argue the simplified framework interpretation can
serve as a bridge to model identification in the hopeful detection of a
new-physics signal. As an illustration, we perform a first determination of the
likelihood that, in the presence of a new-physics signal in a detector like the
DUNE ND-GAr, multiple different new-physics hypotheses (such as the
Higgs-Portal Scalar and Heavy Neutral Lepton ones) can be disentangled. We
demonstrate that this model discrimination is favorable for some portions of
detectable new-physics parameter space but for others, it is more challenging.
