Jimmy, also a bit thick in his own way, doesn't think to introduce himself at first- until/if it becomes obvious that Sirius is drawing a blank. From there he's chatty about Quidditch and cars (and especially bikes). He asks who Sirius wants to win the Quidditch Cup this year.
Jimmy really tries to step up to amuse Dylan. He patiently shows him all the most quality Quidditch gear he can name. He lets Dylan swing his new bat- outside of course, or at least well away from anything breakable. He asks if Dylan has ever been on a broomstick. If Sirius allows it, Jimmy lets Dylan ride on his shoulders and pretends to be a broom for Dylan.