  We study the processes $\gamma \gamma \to K^0_S K^{\pm}\pi^{\mp}$ and $\gamma
\gamma \to K^+ K^- \pi^0$ using a data sample of 519~$fb^{-1}$ recorded with
the BaBar detector operating at the SLAC PEP-II asymmetric-energy $e^+ e^-$
collider at center-of-mass energies at and near the $\Upsilon(nS)$ ($n =
2,3,4$) resonances. We observe $\eta_c$ decays to both final states and perform
Dalitz plot analyses using a model-independent partial wave analysis technique.
This allows a model-independent measurement of the mass-dependence of the
$I=1/2$ $K \pi$ $\mathcal{S}$-wave amplitude and phase. A comparison between
the present measurement and those from previous experiments indicates similar
behaviour for the phase up to a mass of 1.5 $GeV/c^2$. In contrast, the
amplitudes show very marked differences. The data require the presence of a new
$a_0(1950)$ resonance with parameters $m=1931 \pm 14 \pm 22 \ MeV/c^2$ and
$\Gamma=271 \pm 22 \pm 29 \ MeV$.
