I see from your homepage that this may not be an idle request. Cheers!

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?