But in both cases, a "mental process" is required, whereas if the ONLY bright rear red lamp allowed is a brake lamp, there is no ambiguity.
Yes, rear fog lamps "work" because we can process what's going on. Just like red rear turn signals work because we can figure out what's going on after a blink or two.
But if the argument that "yellow means turn and red means stop unambiguously" works for turn signals, and I agree that it does, a bright rear red fog is going to impair response to the brake lamps in EXACTLY the same way that red rear turn signals do (a phenomenon that has already been stated in this thread.) If a study comes out that red rear fogs don't slightly slow recognition of brake lamps in the same way that red rear turn signals do, then I submit that one or the other of the studies is flawed.