Your questions seem related to the 4th point in the video (rhythm) whereas the screenshot displays the 3rd (melody). I'll ignore the screenshot for now.
Are there any guiding principles for when to use pauses in longer form sentences?
AFAIK, no. Hard-coded guidelines related to teaching is provided by the ministry, which may not be the answer you seek.
From the video, this seems to apply to the particle, は, and て form verbs, but is there more to it that I should know?
Yes. You should know (and understand well) the concept of 文節, because 文節 are the potential areas you may take a breath between.
私は / 毎朝 / 8時に / 起きて / 花に / 水を / やって / それから / 学校へ / 行きます
Only then you may decide where to take a breath. You already received two great advice:
- Yosh commented:
the location of the pauses are determined mostly by meaning
- The 4th point of the video says:
take a breath between the important words
Here are extreme examples for the sake of explanation:
- I want to emphasize this is my routine
"私は / 毎朝8時に起きて花に水をやってそれから学校へ行きます。"
- I want to emphasize the daily consistency
"私は / 毎朝 / 8時に起きて花に水をやってそれから学校へ行きます。"
- I want to emphasize the time: 8 o'clock
"私は毎朝 / 8時に / 起きて花に水をやってそれから学校へ行きます。"
- I go to school only after my flower is watered
"私は毎朝8時に起きて花に水をやって / それから / 学校へ行きます。"
And so on. Of course there are more points to consider, but this should be a good starting point.
something I've NEVER seen even mentioned in any class, book, or anything else teaching the language
AFAIK, most kids learn such concept of emphasis during elementary school, at least in Japan, the USA, and the UK in their respective languages.