Although Brooklyn's in no hurry to see his hero Goliath retire, he does dream of someday taking Goliath's place as leader of the clan. Brooklyn is de facto leader of the trio, in that he has the most forceful personality.
Brooklyn probably has an overly romantic idea of what being a leader is all about. He's a big fan of mystery, adventure and battle, etc. But he didn't necessarily understand the hardship that went with leadership, until most of his clan was massacred. Now he wants to prove that he can be a truly great leader. He's probably the most pro-active of all the gargoyles, including Goliath. He has a tendency to look for trouble. He feeds on excitement and conflict. He tends to get in over his head, but the audience should feel that someday, he'll make a wise leader.
Brooklyn sees that the ability to successfully interact with humans is an important asset to a leader, so for that reason, he's the most likely to try to act human. He might put on sunglasses (even at night) or try to ride a motorcycle, etc. That makes human rejection all the more painful when it happens. And it happens often.
As a warrior, he's not the strongest of the trio. But he's the fastest and the savviest. And the most determined.