We study the processes γγ → K þ K − η and γγ → K þ 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 þ e − collider at center-of-mass energies at and near the ϒðnSÞ (n ¼ 2; 3; 4) resonances. We observe η c → K þ K − π 0 and η c → K þ K − η decays, measure their relative branching fraction, and perform a Dalitz plot analysis for each decay. We observe the K Ã 0 ð1430Þ → Kη decay and measure its branching fraction relative to the Kπ decay mode to be RðK Ã 0 ð1430ÞÞ ¼ BðK Ã 0 ð1430Þ→KηÞ BðK Ã 0 ð1430Þ→KπÞ ¼ 0.092 AE 0.025 þ0.010 −0.025 . The η c → K þ K − η and K Ã 0 ð1430Þ → Kη results correspond to the first observations of these channels. The data also show evidence for η c ð2SÞ → K þ K − π 0 and first evidence for η c ð2SÞ → K þ K − η.