  Two mechanisms for the $\pi_1$ ($J^{PC}=1^{-+}$) hybrid meson decay processes
$\pi_1\to\eta\pi,\eta'\pi$ are investigated. These mechanisms are applied to
$\phi\to\eta\gamma,\eta'\gamma$ and $J/\psi\to\eta\gamma,\eta'\gamma$ decays to
illustrate the validity of the decay mechanisms and to obtain independent
information on the coupling of $\eta,\eta'$ to quark and gluonic operators.
  From this information, we find that
$\Gamma(\pi_1\to\eta\pi)/\Gamma(\pi_1\to\eta'\pi)$ is substantially different
in the two decay mechanisms, and hence future experimental measurements of this
ratio will provide valuable information for substantiating the hybrid nature of
these states and for determining the mechanism for these hybrid decays.
