Why is there a difference of the position of Selichot?

Question

In name of my astute oldest son (Yes, as a father, I am biased!):

Why during most fast days is Selichot said after the repetition of the Amidah, but during 10 days of Teshuva, they are said before Shacharit (or after midnight, after Ma'ariv, etc.)?

Answer 1

As you can see from the Tur 581 and his commentators and successors, the Elul/Tishrei Selichot are said pre-dawn as pre-dawn is an auspicious time for connecting with The Spiritual. (See the first Siman in O"C, for other examples of pre-dawn activities.)

^{Recently these have been moved from pre-dawn to midnight, before Shacharit and other random/convenient times, but they belong to pre-dawn, and are still said then by many Vasikin Minyanim.}

The regular fast-day Selichot are in the Amida - in Slach-Lanu - as this is the Bracha dealing with asking for forgiveness; a major theme of any fast day. It's also reminiscent of the extra 6 Brachot that were inserted during drought years between Go'el & Rofeh, as documented in Taanis starting from Mishna 2:2

Others wait until after the Amida, an age-long argument documented in the Tur O"C 566 already, as to whether it's appropriate to have an addition longer than the entire Amida inserted at this point.