Symbolism, Imagery, Allegory
No need to hunt for the perfect good luck charm because Billy has found it: the pearl. He got this little nugget from Ms. Silver because it's the Year of the Dragon, and according to Chinese tradition, the dragon is associated with a pearl. So now Billy has this awesome pearl that he gets to hang onto. Oh, and he gets to make his sister super envious of it.
So since Sal loves the pearl so much, it actually becomes super important in her and Billy's relationship. And that can be a bad thing and a good thing all at once.
The Bad: Dear Pearl, I'd Like to Steal You From My Brother
On the one hand, the pearl reminds us that Billy knows he's older than his little sis so he can trick her into helping him out. Plus, she thinks the pearl is magic and he knows it's not. So when Billy wants Sal to stay up all night with him, he uses the pearl as little sister bait:
He kept holding up the pearl as if it were a priceless gem, turning it between his fingers, hypnotizing her with it. (3.4.14)
It looks like Billy has taken up a side job as a sorcerer. He knows that Sal loves the pearl so he's treating it as if the pearl gives him magical powers to control his sister. And boy is he taking full advantage. Check out how we're told he's "hypnotizing" Sal, as if she almost has no choice but do his bidding. Tsk tsk, Billy Miller. That's some serious manipulation.
The Good: A Bond Made With a Pearl Is Hard to Break
So even though Billy uses the pearl to exploit his little sis's jealousy, he also uses it for good. In fact, after Sal tries to help Billy stay up all night, he turns the pearl into a seriously thoughtful gift:
Billy's forehead wrinkled in thought. These were the things he was thinking: I don't really care about the pearl. Sal helped me last night—but I can't tell her that. If I give her the pearl, it would be a way to thank her without having to say anything. (3.5.35)
Nice gesture, right? He and Sal didn't even meet their goal of pulling an all-nighter and he still wants to reward his little sister. Plus, not only does this pearl create a super tight bond between these siblings, but it also shows us that they have a special way of communicating. No need for words here, because they have a snazzy pearl instead.
So the pearl is about both manipulating his sis a bit, and forming a bond with her. Not too shabby for a shiny little thing.