  The Cs$_2$LiYCl$_6$:Ce (CLYC) elpasolite scintillator is known for its
response to fast and thermal neutrons along with good $\gamma$-ray energy
resolution. While the $^{35}$Cl($n,p$) reaction has been identified as a
potential means for CLYC-based fast neutron spectroscopy in the absence of
time-of-flight (TOF), previous efforts to functionalize CLYC as a fast neutron
spectrometer have been thwarted by the inability to isolate proton interactions
from $^{6}$Li($n,\alpha$) and $^{35}$Cl($n,\alpha$) signals. This work
introduces a new approach to particle discrimination in CLYC for fission
spectrum neutrons using a multi-gate charge integration algorithm that provides
excellent separation between protons and heavier charged particles. Neutron TOF
data were collected using a $^{252}$Cf source, an array of EJ-309 organic
liquid scintillators, and a $^6$Li-enriched CLYC scintillator outfitted with
fast electronics. Modal waveforms were constructed corresponding to the
different reaction channels, revealing significant differences in the pulse
characteristics of protons and heavier charged particles at ultrafast, fast,
and intermediate time scales. These findings informed the design of a pulse
shape discrimination algorithm, which was validated using the TOF data. This
study also proposes an iterative subtraction method to mitigate contributions
from confounding reaction channels in proton and heavier charged particle pulse
height spectra, opening the door for CLYC-based fast neutron and $\gamma$-ray
spectroscopy while preserving sensitivity to thermal neutron capture signals.
