  In this paper we improve and extend a recent analysis which showed that the
rho-omega mixing amplitude cannot be unambiguously extracted from the pion
electromagnetic form-factor in a model independent way. In particular, we focus
on the argument that the extraction is sensitive to the presence of any
intrinsic omega_I -> pi pi coupling. Our extended analysis confirms the
original conclusion, with only minor, quantitative differences. The extracted
mixing amplitude is shown to be sensitive to both the intrinsic coupling
omega_I -> pi pi and to the value assumed for the mass of the rho^0-meson.
