Using a setup for testing a prototype for a satellite-borne cosmic-ray ion detector, we have operated a stack of scintillator and silicon detectors on top of the Princess Sirindhorn Neutron Monitor (PSNM), an NM64 detector at 2560-m altitude at Doi Inthanon, Thailand (18.59 N, 98.49 E). Monte Carlo simulations 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 particles from cosmic ray showers, which can be detected by the scintillator and silicon detectors. Those detectors can provide a timing trigger for measurement of the propagation time distribution of such neutrons as they scatter and propagate through the NM64, processes that are similar whether the interaction was initiated by an energetic proton (for 15% of the count rate) or neutron (for 80% of the count rate). This propagation time distribution underlies the time delay distribution between successive neutron counts, from which we can determine the leader fraction (inverse multiplicity), which has been used to monitor Galactic cosmic ray spectral variations over $sim$1-40 GV. Here we have measured and characterized the propagation time distribution from both the experimental setup and Monte Carlo simulations of atmospheric secondary particle detection. We confirm a known propagation time distribution with a peak (at $approx$70 microseconds) and tail over a few ms, dominated by neutron counts. We fit this distribution using an analytic model of neutron diffusion and absorption, for both experimental and Monte Carlo results. In addition we identify a group of prompt neutron monitor pulses that arrive within 20 microseconds of the charged-particle trigger, of which a substantial fraction can be attributed to charged-particle ionization in a proportional counter, according to both experimental and Monte Carlo ...
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