Strong evidence exists that the quark--gluon plasma, a deconfined state of quarks and gluons created in heavy-ion collisions, exhibits a strong collective behavior. A similar collective behavior has also been observed in small collision systems. To study the origin of collectivity in small collision systems, the second order Fourier coefficient $v_2$ of inclusive charged particles and \pipm{}, \kapm{}, and p+\pbar{} is measured in pp collisions at $\sqrt{s} = 13.6$ TeV and p--Pb collisions at $\sqrt{s_{\rm NN}} = 5.02$ TeV simulated with different configurations of PYTHIA8 and EPOS4 event generators. Results obtained using the scalar product and cumulant methods are reported as a function of transverse momentum $p_{\rm T}$ in different multiplicity classes and as a function of charged-particle multiplicity $N_{\rm ch}$, respectively. A strong dependence on $N_{\rm ch}$ is found for the second order two-particle cumulants, while the second order four-particle cumulants are consistent with zero. The $v_2$ of identified particles increases with the multiplicity class, being mass-ordered at low $p_{\rm T}$ for the 0--5\% multiplicity class when a large $|\Delta\eta|$ gap is employed to suppress contributions from few-particle correlations.