  We extend a recent calculation of the momentum dependence of the
$\rho-\omega$ mixing amplitude to the pseudoscalar sector. The $\pi\!-\!\eta$
mixing amplitude is calculated in a hadronic model where the mixing is driven
by the neutron-proton mass difference. Closed-form analytic expressions are
presented in terms of a few nucleon-meson parameters. The observed momentum
dependence of the mixing amplitude is strong enough as to question earlier
calculations of charge-symmetry-breaking observables based on the on-shell
assumption. The momentum dependence of the $\pi\!-\!\eta$ amplitude is,
however, practically identical to the one recently predicted for $\rho-\omega$
mixing. Hence, in this model, the ratio of pseudoscalar to vector mixing
amplitudes is, to a good approximation, a constant solely determined from
nucleon-meson coupling constants. Furthermore, by selecting these parameters in
accordance with charge-symmetry-conserving data and SU(3)-flavor symmetry, we
reproduce the momentum dependence of the $\pi\!-\!\eta$ mixing amplitude
predicted from chiral perturbation theory. Alternatively, one can use
chiral-perturbation-theory results to set stringent limits on the value of the
$NN\eta$ coupling constant.
