I don't know this sub-area very well, and esp not the methodology. My understanding wrt Big-5 (which is the best studied and most thoroughly validated, though there are a number of more modern extensions of it) was close to your account, but had a few steps flipped:
  • Ask shit ton of questions
  • Do a factor analysis / PCA variant
  • Pick a number of factors that seems like the right number based on unexplained variance
  • Figure out how different questions load on those factors
  • Name them
But as you suggest, the magic is deciding how many types of things you want there to be. Wrt Big 5, you can make some reasonably interesting inferences based on neural primitives, so I think it's useful. Some clinicians make a lot of it.
That Jordan Peterson writing exercise that I posted about a couple months ago and can't find now for some reason (here's the website) is actually a quite good version of this -- before he became a culture war figure, JBP did a lot of very strong work in personality psychology. Highly recommended if you're into stuff like this, @cryotosensei.
Bookmarked your comment. See, sometimes exploring weird random shit pays off haha
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Thanks for clarifying that a bit. It's been a while since I covered this in my stats classes and it's not something I've used in my own work.
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