We study the processes γ γ → K 0 S K ± π ∓ and γ γ → K + K − π 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 Υ ( n S ) ( n = 2 , 3, 4) resonances. We observe η 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 π   S -wave amplitude and phase. A comparison between the present measurement and those from previous experiments indicates similar behavior 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 ± 14 ± 22     MeV / c 2 and Γ = 271 ± 22 ± 29     MeV .