
Let me reply to your questions in reverse order.
> What convinced you that it is rigorous?
I originally stumbled across some books on (the other) NLP and they just made sense, and the "algorithms" they described worked. I had some emotional issues and used the techniques to overcome them to some degree. I also carried out informal experiments, mostly on myself but occasionally with friends, to double check that I wasn't fooling myself. I suffered from pretty severe depression that interfered with living a normal life (I was homeless for a few years after high school) Eventually, I managed to go see one of the co-founders of NLP, Richard Bandler, and he cured my depression in a single ten-minute intervention. (I know how that sounds, but it's true. I've written about it once or twice before in comments here on HN if you want more details, or just ask.)
So that pretty much clinched it for me. After my depression was cured I went on to have a fairly successful career as a programmer, and I am more-or-less a functioning adult thanks to Bandler. But I also lost interest in NLP personally (I mean, I still use what I've learned, but I don't feel called to be a therapist or anything like that.) I mention it from time to time because what kind of a monster would I be if I didn't? But I often get flak for it. (One fellow on here has called me a liar, fool, and scammer for talking about getting cured of depression.)
When I say that the material "made sense" I don't mean merely that it sounded plausible, I mean that it was similar to electronics or mathematics: there are formal patterns in the structure of subjective experience, and we can learn to notice and deliberately manipulate those patterns in repeatable codified algorithms. (E.g. the "Five-Minute Phobia Cure" pattern, which eliminates phobic responses quickly and durably (the phobia never comes back.))
The original work grew out of linguistic analysis of particularly effective therapists (Satir, Perls, Erikson), they were literally transcribing therapy sessions and started applying ideas from Chomsky's Transformational Grammar.
> What resources could you provide on this for a skeptical cognitive scientist?
First of all, I'm sorry to say that most of the stuff on the Internet about (the other) NLP seems to be fluffy and nonscientific (to put it politely). If I'm being frank, I don't think most people practicing NLP understand it very well from a scientific viewpoint.
I would recommend going to the source. Find and read "The Structure of Magic" (both volumes but especially the first, which explores linguistic patterns, the second volume then generalizes to the sensory channels.) You're probably going to be interested in what they call the "Meta Model" which is a set of questions designed to elicit elided information in a therapeutic setting.
Beyond that I don't really have any recommendations. It really depends on what you want to do. You might enjoy "Trance-FORMATIONS" which is IMO one of the best books on hypnosis ever written, it's all about how language affects and guides the mind. I suppose you could also go take a class or course?
https://www.amazon.com/Trance-Formations-Neuro-Linguistic-Pr...
FWIW, some books. "Structure of Magic" I & II are the first two books and are a good place to start from to see the origins of the latter work. TRANCE-Formations is a rich text on theraputic hypnosis. And then there's the Core Transformation Process, an algorithm for profound spiritual growth.
https://www.goodreads.com/book/show/964154.The_Structure_of_...
https://www.goodreads.com/book/show/821993.The_Structure_of_...
https://www.goodreads.com/book/show/956297.Trance_Formations
https://www.goodreads.com/book/show/369813.Core_Transformati...
As for self-hypnosis, you can learn it from a book or a website, but you might also want to check out the people locally who are into hypnosis and self-improvement.
Personally, I get really good results from a very simple induction. It has a lot of names, "Betty Erickson’s Induction", "See, Hear, Feel Induction", "5-4-3-2-1 Induction", and so on. It's easy to remember and reliable. This is a good write-up of the process: https://www.practicalhappiness.co.uk/media/download_gallery/...
That should be enough to get you started.
FWIW, although I'm not a hypnotist I know a lot about it, AMA.
For "higher" states of consciousness there is actually a simple and effective algorithm called "Core Transformation Process" It's taught by these folks: https://www.coretransformation.org/
For the deeper spiritual aspects of psychological healing I can recommend the works of Sir David R. Hawkins, M.D., Ph.D., who was a very successful therapist who underwent enlightenment and has been able to describe it in terms accessible to the modern mind. https://veritaspub.com/dr-hawkins/#Biography%20Summary
For specifically improving "cognitive enhancement" the easiest, safest, and most far-reaching technique involves modifying your self-image. You can reprogram yourself to believe that you're smarter and your mind will modify your behaviour to meet your belief. For better or worse one's intelligence level is generally tied into one's self-image, and the only barrier to being smarter is your natural reluctance to become a different person.
For self-image engineering the best books I've found are "Psycho Cybernetics" by Maltz and "With Winning in Mind" by Bassham.
https://www.goodreads.com/book/show/447454.Monsters_and_Magi...
https://www.goodreads.com/book/show/956297.Trance_Formations
https://www.goodreads.com/book/show/155981.Psycho_Cybernetic...
https://www.goodreads.com/book/show/208926.With_Winning_in_M...
(But really, read "Prometheus Rising" by R. A. Wilson and do the exercises.)
