Well, he did only attempt 9 of his 36 FGAs (25%) in the games where he played under 10 minutes, so it's not like he was blackholing garbage time. He just wasn't, as they say, put in a position to succeed. But really, how much of his shot selection was the teams not caring to utilize his strengths and how much of it was his own decision/out of frustration is tough to say. I'd hope it's mostly the former.
Either way, Brown needs to make 100% sure that Noel is not used as a jump shooter. Some of that is to tell him not to take them. Some of that is drawing up plays to get him shots at the rim at least often enough to keep him satisfied. Other than that, grab rebounds, block shots, deflect balls, and generally make scoring hard for the other team - that's all we need.
Anyway, hopefully that fact that he's 29 and it is beginning to look like NBA teams aren't exactly knocking down his door for his services will at least clue him in to the idea that he needs to buy in to his role.