The main evidence of who Ishmael is—and by extension his reliability as a narrator—takes place during the first part of the story where he actually talks about himself and his actions. After that, he sort of fades into the background.
Ishmael’s relationship with Queequeg seems to me strange, because of Ishmael’s initial reaction. It’s almost as if he’s a greenhorn, with no experience of the sea and in awe of everything around him, especially those of different cultures, rather than someone who has been to sea before—as Ishmael claims. And yet if I disregard Ishmael’s assertion that he has been to sea before and is simply looking for a different ship, then that may explain his complete ignorance to seafaring life, but not his immediate acceptance of Queequeg as a friend and equal in a time when a colored man would be treated as a servant or property.