Some independent sources talking about the sun's path on the equinox.
"Everyone along Earth’s equator on the day of the equinox – and for a day or two before and after it – will experience that noonday sun more or less overhead."
http://earthsky.org/tonight/sun-over-earths-equator-at-equinox"Imagine standing at the equator. At point A you are positioned in the middle of the nighttime side of the globe; it is midnight at Point A. 6 hours later you will be standing at Point B where you will move from night to day; this is sunrise. To see the sun you must look exactly back along one of the rays of light coming from the sun. You must turn and look straight east to do this. One the equinoxes, the sun will rise in the east (not just somewhere in the east but exactly due east). This only happens on the spring and fall equinox. The rest of the year the sun will rise south or north of east."
http://www.atmo.arizona.edu/students/courselinks/fall07/nats101s31/lecture_notes/sunpaths.html"In late March and late September (at the "equinoxes"), the sun's path follows the celestial equator. It then rises directly east and sets directly west."
https://physics.weber.edu/schroeder/ua/sunandseasons.htmlThese are theoretical discussions of what will happen in the future and for all time. The pattern and understanding of the sun's path on the equator on the equinox well understood based on thousands of years of observation. The pattern is completely consistent and predictable.
The polar regions are exceptional because there are the only place where ease and west don't apply the same. If you are exactly on the north pole, by definition, every direction is due south. Observation #4 would not apply. I'm not sure how to correctly refer to the south pole when considering the AE map as the south pole can be considered to be a line of circumference. That's clearly not what is meant by a pole. Maybe just calling it a "polar region" is satisfactory. I'm not certain exactly how large to consider this area (north or south). Excluding the entire Arctic and Antarctic circles seems to be excessive, but probably fine for this map consideration. There are other simple observations that can be added regarding these regions.
At this point I am completely satisfied that observations #1, #4 and #5 are accurate for all locations on earth outside the polar regions. As #5 represents a subset of #4, I will drop it from the list and add a caveat regarding the polar regions. The current list of observations:
1. on the equinox the sun traces a very nearly straight line across the sky for every location on the equator.
2. on the northern solstice the sun is very nearly directly almost overhead at solar noon for every location on the tropic of cancer.
3. on the southern solstice the sun is very nearly directly overhead at solar noon for every location on the tropic of capricorn.
4. on the equinox the sun rises almost exactly due east and sets almost exactly due west for every location on the earth, except for the polar regions.