[...Is Heiji just the living Osakan stereotype or something? Though it does at least work in their favor.]

Then next time you get a chance, could you ask him about it? I think it would be less suspicious if you talked to him.

[Because let's be real here, Sasuke has more or less established a pattern of wandering off on his own; it may just pique their host's interest if he was the one to approach Heiji about it out of the blue.]