I insisted that he doesn’t look out of the window.
I insisted that he don’t look out of the window.
I insisted that he not look out of the window.
Which is correct?
I insisted that he doesn’t look out of the window.
I insisted that he don’t look out of the window.
I insisted that he not look out of the window.
Which is correct?
You could say 1. if you've noticed that he doesn't look out of the window, and you're insistently telling someone else this.
If you're insistently telling someone else to make sure that he doesn't look out of the window [in future], then say 3.
All three are used in everyday language (prescriptive vs descriptive argument can begin), but I'd lean to number 3 being the (prescriptively) correct one because you insisted something. Ie. What follows is a noun clause and therefore shouldn't have a fully conjugated subject/verb pattern.
Number 2 is a clear case of subjunctive:
I insist he do/do not continue.
However, it is nowadays considered so overcorrect that it has known a decline in use.
As for nr 1, although the grammar books will tell you that it not correct, this is the one structure most people use nowadays. So much so, that to some native speakers number 2 appears to sound incorrect.