Your initial impulse is much better than what you are saying here. It's much better to understand the principles behind the "rules" than it is to follow a list by rote, and you were exactly right to ask about principles. So, let’s derive some principles, shall we? Below is a four part realization in the key of A minor for every instance Sessions lists, followed by an explanation for those I can explain. If you just want the conclusion, the things you need to remember, see the bold bit at the bottom.
Minor mode.jpg
1. This is a typical deceptive resolution, so of course the Leading tone G# must go to A
2. If the G were sharped, there would be motion by an augmented 2nd, a prohibited interval.
3. I don’t get 3 & 4. Think I’d have to see these in a larger context. The leap of a tritone in the bass in example 4 could make sense if it were part of a sequence of similar leaps(?)
4.
5. If the G were sharped, there would be motion by an augmented 2nd, a prohibited interval.
6. If the G# went down to F it would be a prohibited augmented 2nd.
7. If the G were sharped, there would be motion by an augmented 2nd, a prohibited interval.
8. If the F weren’t raised it would be motion by an augmented 2nd
9. If the F were natural there would be motion by an augmented 2nd. If both were natural the succession of 6 chords would be weak in the bass.
10. If the F were sharped, there would be motion by and augmented 4th in the bass, an interval usually avoided.
11. F# would be out of key — we’re going to the relative major here, so F-natural makes sense (is in key).
12. See 11. If it isn’t going to continue through G#, there will almost never be an F#. See examples 8 & 9 where the two accidentals are properly paired.
13. F isn’t going to turn into F# in this kind of basic diatonic grammar.
So, the main principle seems to be: motions by augmented intervals are outside the voice-leading norms of common practice music. Eight of the above rules can be retired if one simply remembers: Don’t write augmented intervals in diatonic progressions!
The second principle can be stated two ways: 1) don’t raise the 6th without raising the 7th right after it. 2) Don’t sharp the F when you’re clearly hanging out in the relative major.
So, to comply with Sessions’ rules you only need to remember two things:
1) Avoid motion by augmented intervals.
2) Don’t raise 6 without also raising 7 (or, don’t raise 6 when you’re in (flirting with) the relative major.)