He's a fox.
He's a spy.
Got a little side tracked while waiting for the system to get me reply. I really loved your comment a lot. I'm glad I'm not the only one who hates the hat bob. I didn't think it was good at any point in time. Was hoping I'd warm up to it. That's still a definite nope.
His coat collar was actually meant to also bob up and down, too, but I somehow screwed up somewhere along the line, and it got completely missed, even though it existed in the flat-color staged just before shading, and then I just didn't bother to go back and fix it.
You're also right about the flap movement for another reason: the type of hat used by detectives of the era were fairly stiff-brimmed, so the flop of it wouldn't make sense. I think I'll chuck the hat movement entirely.
There's a lot to like here. The legs receding into shadow as they push back; the left side of the jacket sinking into and out of shadow as the torso pivots left to right; the amount of pivot being noticeable but still subtle for a cartoon movement, selling an attitude that isn't hammy or overexaggerated; the subtle subpixelling on the ears and right side of the face; the nonchalant tail movement. It's hard to argue with. Mostly the brim of the hat flopping up and down doesn't seem to compliment the rest of the animation; it feels that motion would fit on a character whose whole jacket is also bobbing up and down following after the character's motion, like a Disney pastiche of a detective.