---How would the male garibaldi's behavior impress a female...what qualities might she look for?

If you answered that his swooping and dipping and loud 'thumping' noises (made with his teeth!) would tell her something about his defensive capabilities, you are correct! Not only would he attract her attention with his movement and sounds, but the energetic active 'workout' of his display would give her an idea of how much energy he might devote to protecting the eggs and eventually the babies, from other fish that want to eat them.  So the more active and the better show that the male puts on the better the female likes it, and the more likely she will choose him!

There is also another interesting connection with his "home ownership pride!" Researchers have found that the more lush and perfect the algae mat, the better performance the male puts on!  Somehow he knows that she will prefer the more lush mat, and that he is not likely to get chosen if the algae mat is sparse and untended...so why bother with the 'show' if the real estate is not up to the market value?!