We analyze the second-class current decays $tau^{-}topi^{-}eta^{(prime)} u_{tau}$ in the framework of Chiral Perturbation Theory with resonances. Taking into account $pi^{0}$-$eta$-$eta^{prime}$ mixing, the $pi^{-}eta^{(prime)}$ vector form factor is extracted, in a model-independent way, using existing data on the $pi^{-}pi^{0}$ one. For the participant scalar form factor, we have considered different parameterizations ordered according to their increasing fulfillment of analyticity and unitarity constraints. We start with a Breit-Wigner parameterization dominated by the $a_{0}(980)$ scalar resonance and after we include its excited state, the $a_{0}(1450)$. We follow by an elastic dispersion relation representation through the Omn`{e}s integral. Then, we illustrate a method to derive a closed-form expression for the $pi^{-}eta$, $pi^{-}eta^{prime}$ (and $K^{-}K^{0}$) scalar form factors in a coupled-channels treatment. Finally, predictions for the branching ratios and spectra are discussed emphasizing the error analysis. An interesting result of this study is that both $tau^{-}topi^{-}eta^{(prime)} u_{tau}$ decay channels are promising for the soon discovery of second-class currents at Belle-II. We also predict the relevant observables for the partner $eta^{(prime)}_{ell 3}$ decays, which are extremely suppressed in the Standard Model.
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