We performed a theoretical analysis of the semileptonic decays $\eta^{(\prime)}\to \pi^0 \ell^+\ell^-$ and $\eta^{\prime}\to \eta \ell^+\ell^-$, where $\ell=e,\mu$, via a charge-conjugation-conserving two-photon mechanism. The underlying form factors are modelled using vector-meson dominance, phenomenological input, and U(3) flavour symmetry. We considered both a monopole and a dipole model, the latter tailored such that the expected high-energy behaviour is ensured. Furthermore, we benchmarked the effect of $S$-wave rescattering contributions to the decays. We inferred significant effects from the form factors neglected in the literature so far, still finding branching ratios of the various decays well below the current experimental upper limits.