  Recently, the PHENIX Collaboration has published second- and third-harmonic
Fourier coefficients $v_2$ and $v_3$ for midrapidity ($|\eta|<0.35$) charged
hadrons in 0\%--5\% central $p$$+$Au, $d$$+$Au, and $^3$He$+$Au collisions at
$\sqrt{s_{_{NN}}}=200$ GeV utilizing three sets of two-particle correlations
for two detector combinations with different pseudorapidity acceptance [Phys.
Rev. C {\bf 105}, 024901 (2022)]. This paper extends these measurements of
$v_2$ to all centralities in $p$$+$Au, $d$$+$Au, and $^3$He$+$Au collisions, as
well as $p$$+$$p$ collisions, as a function of transverse momentum ($p_T$) and
event multiplicity. The kinematic dependence of $v_2$ is quantified as the
ratio $R$ of $v_2$ between the two detector combinations as a function of event
multiplicity for $0.5$$<$$p_T$$<$$1$ and $2$$<$$p_T$$<$$2.5$ GeV/$c$. A
multiphase-transport (AMPT) model can reproduce the observed $v_2$ in
most-central to midcentral $d$$+$Au and $^3$He$+$Au collisions. However, the
AMPT model systematically overestimates the measurements in $p$$+$$p$,
$p$$+$Au, and peripheral $d$$+$Au and $^3$He$+$Au collisions, indicating a
higher nonflow contribution in AMPT than in the experimental data. The AMPT
model fails to describe the observed $R$ for $0.5$$<$$p_T$$<$$1$ GeV/$c$, but
there is qualitative agreement with the measurements for $2$$<$$p_T$$<$$2.5$
GeV/$c$.
