Your very clear photos show a red-white pair coming from a power source and going to a light fixture, with a switch inserted into the red (hot) lead. You have to figure out which pair (which conduit, left or right) is coming from the power source and which one is going to the light fixture. Use a probe capable of piercing the insulation on the white wire (or just cut it, since you have to cut it anyway to install the GFCI outlet). Turn off the light and measure the voltage between the white wire and each of the red wires. The red-white pair that has voltage on it is the pair coming from the power source. Switch off the circuit breaker and connect this red-white pair to the Line terminals of the GFCI. Connect the white wire from the light fixture to the white wire on the GFCI. Connect the switch between the red wire coming from the light fixture and the red wire on the GFCI. You're right, the lack of a ground wire is OK; a GFCI can be used for a two-wire outlet. See the sketches below. The hardest part of this job will be enlarging the opening in the tile without cracking adjacent tiles, removing the single box, and installing a double box for the GFCI outlet and switch.