  We have studied the $\tau^-\to K^-\eta^{(\prime)}\nu_\tau$ decays within
Chiral Perturbation Theory including resonances as explicit degrees of freedom.
We have considered three different form factors according to treatment of
final-state interactions. In increasing degree of soundness: Breit-Wigner,
exponential resummation and dispersive representation. We find that although
the first one fails in accounting for the data on the $K\eta$ mode, the other
two approaches provide good fits to them which are sensitive to the
$K^\star(1410)$ pole parameters, that are determined to be
$M_{K^{\star\prime}}\,=\,(1330^{+27}_{-41})$ MeV and
$\Gamma_{K^{\star\prime}}\,=\,(217^{+68}_{-122})$ MeV. These values are
competitive with the standard determination from $\tau^-\to(K\pi)^-\nu_\tau$
decays. The corresponding predictions for the $\tau^-\to
K^-\eta^{\prime}\nu_\tau$ channel respect the current upper bound and hint to
the discovery of this decay mode in the near future.
