The diagram and path of light you provided above seems very similar to the one I made.
Why do you guys keep trying to connect Argentina to some point on the surface of the earth?
You're trying to understand how the sun can appear along a given bearing at sunset/rise, correct? Connecting the location on a globe earth where the sun appears on the horizon with the location on a globe earth where the sun is directly overhead gives you that bearing.
Consider what you guys are saying happens at Equinox, for example. The sun is over the equator, and you tell us that someone in Miami would see the sun rising from directly East. The sun (allegedly) rises directly from the East. Right?
Yet, if we used your method of connecting Miami along the surface of the globe, over to where the sun is directly over the equator, the observer would be looking to the South of East.
If this surface of the earth method is accurate, how would you explain the above?
I did exactly what you told us was necessary to get the bearing of the sun. I made a line between Miami and the Equator, to where the sun is most directly over. Yet the rays of the sun are still coming in from the East.
It seems clear, to me, that these would have to be lines that stretch out into space to depict this, not along the surface of a globe. If the above analogy is valid, then it suggests that all of the illustrations of the observer-to-sun paths along the surface of the globe, including the one in the first post of your OP, are in question.
This directly answers your question in the OP in regards to bearings and the surface-of-the-earth method of sun bearing that is used.