I can’t seem to find information regarding what the accepted brain functions are that for the electrode placements. I know these represent AF7, AF8 (or F7 and F8 depending upon head size) TP9 and TP10, but what neuro-cognitive functions are associated specifically with these points?
I think one of the reasons you’re unable to find generally accepted brain functions for specific electrodes is there simply isn’t one yet. EEG isn’t very good at spatially isolating where in the brain activity is coming from so there is a risk that an electrode may be registering activity coming from elsewhere in the brain.
You’ll find qEEG studies and sites that claim to offer rough estimates of what electrodes correspond to what mental activities but I’d be skeptical if I were you. Below is a rough map that shows what areas of the brain process certain kinds of sensory data and what parts are related to higher functioning. As I mentioned, given how spatially inaccurate EEG is, it’s not as simple as mapping things out clearly like the picture below, although it does offer a good starting point.