When and how did the culture divide between Normans and Sicilians dissipate? Or did it? I'm aware of Roger d'Hauteville's line of kings and the relative harmony between all of the cultures living on the island (Muslims, Greeks, Italians, Normans) but I imagine at some point the inhabitants (whether lord or commoner) began to think of themselves as more Italian than anything else. So when did the Normans, first mercenaries and then ruling elite/warrior class, stop identifying as Norman?
The Hauteville Normans stopped self-identifying as Norman pretty early on, in my view. It's difficult to say with any degree of certainty because no one jotted down a handy 'I am Norman' or 'I am not Norman' note at any point. We have to deduce the degree to which they considered themselves Norman based on the way the kings/counts/dukes referred to themselves in official diplomata and the extent to which they used recognisably Norman cultural or administrative features.
I gave a more detailed answer, which you might find useful, in response to similar question over here.