I actually watched this movie again recently (yeah... I go to monthly showings) and I just can't see Brad as ESTJ. ISTJ is more probable.
One key trait of his is that he never actually does anything, just reacts to what is going on around him. If he were ESTJ, I think he'd be far more assertive, since ESTJs are people big on putting thoughts into action.
I am still new to MBTI so I could have it all wrong, but that bit was sticking out to me.