  The momemtum dependence of the off-shell $\rho$-$\omega$ mixing amplitude is
calculated through a two-quark loop diagram, using non-perturbative meson-quark
vertex functions for the $\rho$ and $\omega$ mesons, as well as
non-perturbative quark propagators. Both these quantities are generated
self-consistently through an interlinked BSE-cum-SDE approach with a 3D support
for the BSE kernel with two basic constants which are pre- checked against a
wide cross section of both meson and baryon spectra within a common structural
framework for their respective 3D BSE's. With this pre-calibration, the
on-shell strength works out at -2.434$\delta(m_q^2)$ in units of the change in
"constituent mass squared", which is consistent with the $e^+e^-$ to
$\pi^+\pi^-$ data for a u-d mass difference of ~4 MeV ,while the relative
off-shell strength (0.99 $\pm$ 0.01) lies midway between quark-loop and QCD-SR
results. We also calculate the photon-mediated $\rho$-$\omega$ propagator whose
off-shell structure has an additional pole at $q^2$=0. The implications of
these results vis-a-vis related investigations are discussed.
