Call me suspicious.
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.
As for the type of relationship they have, I’m not convinced that this “bosom friendship” is very deep, since they don’t communicate very well. Not that words necessarily speak louder that actions, but even when they get onto the Pequod, Ishmael doesn’t mentioned Queequeg individually all that much. It doesn’t seem like they are all that close after Chapter 10. In fact, aside from inform us what the other characters are doing, Ishmael himself doesn’t seem close to anyone.
Take “The Mat Maker” chapter: The entire crew gets involved weaving a swordmat, and the metaphor of the loom could be interpreted as the relationship between fate, free will, and chance.
Ishmael says that he “kept passing and repassing” as Quequeg and the others remained stationary in their tasks. He’s like a shuttle weaving back and forth between static threads. While every individual life on the ship was fixed in place, only Ishmael’s fate is, at that moment, in a state of flux.
Is this guy Ishmael reliable? We know he says “Call me Ishmael,” but is that really his name? He says he’s been to sea before, but doesn’t seem to know the major port of Nantucket all that well. He narrates the ongoing thoughts of Ahab and Starbuck among others, while he as a character is entirely passive, almost completely fading from the activity of the Pequod.
So, barring Melville’s awkward use of the novel genre—we know it’s his first novel, and he sometimes incorporates elements of drama—either Ishmael has some mental-telepathy thing going on, or maybe he doesn’t really exist at all. That is, he doesn’t exist in the same way the other characters exist. It’s like he’s on another plane of reality, in a way that transcends identity, which is why he identified with Queequeg and Ahab and knows everyone’s innermost thoughts. It’s like he’s a phantom, which makes him being the sole survivor of the Pequod ironic.