I have no idea how TS calculates the sun position or what variables are used and where they are stored, but I do know that the azimuth of the sun (position E of N) at any given time and date is only half of the celestial coordinates needed to define the apparent position of a celestial object in the sky. The other coordinate needed is the altitude (angular position above the horizon).
Using the U.S. Naval Observatory online calculator; on the summer solstice at Chicago, Illinois the sun will reach its highest altitude of 71.6 degrees at 12:50 local time. At that time the azimuth of the sun will be 178.2 degrees, almost due south. On the winter solstice at the same location the sun will reach its highest altitude of 24.7 degrees at 11:50 local time. At that time the azimuth of the sun will be 180.3 degrees, again almost due south.
In the above example it is plain to see two things: Yes, objects will cast a much longer shadow in the winter than they do in the summer at that location due to the sun's low apparent angle in the sky during the winter compared to summer. Secondly, the important variable that changes with the seasons is the
altitude of the sun at local maximum, not the azimuth. By definition the azimuth will remain 180 degrees (the minor differences of the azimuth angle in the examples are caused by extrapolating the resulting calculation to the closest minute) at the maximum local altitude regardless of the season in the northern hemisphere. The variables that will change will be the altitude and the local time that the maximum altitude will be reached.
Azimuth would be the most important variable in defining the apparent position of the sun at times of sunset and sunrise.
Hope this helps.
