I've always had trouble splitting up the ideas of agnosticism and atheism. You inspired me to dig a little into the definitions. Agnostic as a word looks like an adjective in "agnostic atheist" but after reading up on agnostic, agnostic atheist, and atheist, they feel like different points on a spectrum and "agnostic atheist" is a name for one of those points/philosophies instead of being a clear modifier of atheist.

I'd even go so far as to argue against your point about agnosticism not being about belief; it's the belief that we do not and cannot know about the existence of God and consequently do not believe or disbelieve in god. An agnostic atheist doesn't believe we can know about the existence of God but also believes God does not exist.

Even after typing all of this I feel like I'm splitting hairs on the definition of belief. The only thing I'm confident about is that the terms "agnostic" and "gnostic" are too fluid for easy discussion. Even gnostic vs Gnostic (capital G) don't mean the same thing.