I've been studying this "phenom" in the game for a couple of months, obviously to make this post, and one of the most interesting things I've noticed is the fact that the sun does a sort of ellipse in the sky from east to south. Well, that has an explanation: the season & the shape of the map.
The creators made this on purpose, mainly because of the game engine limitations; first of all, we have to accept that the map design isn't too much realistic, just think it, is a square. So, now knowing that, where it fits the "season" reason? during the fours temperate seasons of every year, Summer, Fall (autumn), Winter and Spring, the sun path changes in real-life, so they made this "ellipse" path with the idea of recreating the (probably) Summer season; obviously there are some discrepancies like the fact that people goes to the beach and we can find peds having a sunbath and at the same time, a surprise rain appears, although that last part happens because the game have a calendar, the days pass and we have an infinite cycle.
The problem comes when people convert other game maps to GTA SA because the sun path on those games isn't the same as in GTA SA; for example, when Rockstar Games designed GTA IV, they made it trying to have to closest recreation of the real NYC sun path and the shadows of the city, as we can see in the first trailer.
With GTA V happens the same, if somebody ports the GTA V map to GTASA, the sun path won't be the same, in GTA V, due to the new engine and possibilities, they made a more realistic version of San Andreas (California), almost identical, this time with a proper sun path.
Now you may be thinking "if this so important, why there's no a mod to fix or change that?", the answer is pretty simple: hardcoded. The sun path is unfortunately hard coded in the game .exe and we don't know the exact memory addresses to change it. I've been trying to find those addresses but without help, is a harsh work, I've contacted my friend Junior Djjr, so he could probably help me find out.
To finish this post, as a conclusion we can say that although the sun path isn't too realistic for modern games when they made it, it was planned to work with the game limitations and the game design.