Using a setup for testing a prototype for a satellite-borne cosmic-ray ion detector, we have operateda stack of scintillator and silicon detectors on top of the Princess Sirindhorn Neutron Monitor(PSNM), an 18-counter NM64 detector at 2560-m altitude at Doi Inthanon, Thailand. Monte Carlosimulations have indicated that about 15% of the neutron counts by PSNM are due to interactions(mostly in the lead producer) of GeV-range protons among the atmospheric secondary particlesfrom cosmic ray showers, which can be detected by the scintillator and silicon detectors. Detectionof incoming charged particles associated with neutron counts in the NM64 allows a measurementof the travel time distribution of such neutrons as they scatter and propagate through the NM64,processes that are nearly the same whether the interaction was initiated by an energetic proton (for15% of the count rate) or neutron (for 80% of the count rate). This travel time distribution underliesthe time delay distribution between successive neutron counts, from which we can determine theleader fraction (inverse multiplicity), which has been used to monitor Galactic cosmic ray spectralvariations over∼1-40 GV. In the present experiment we have measured both the coincidence rateof incident charged shower particles with neutron counts in the NM64 and the neutron travel timedistribution. We utilize these measurements to validate Monte Carlo simulations of atmosphericsecondary particle detection by the NM64 and the resulting yield functions used to interpret thecount rate and the leader fraction.