But "gnostic" doesn't mean "I know there is a god." "Gnostic" is an adjective meaning "I have knowledge in regards to [the subject of the adjective]."

Yes, but we aren't talking about the term "gnostic", we are talking about the term "gnostic atheist." If the subject of the adjective is "Does god exist?", then saying "I know that is not the case" does mean "I know there is no god."

Literally every person I have ever heard define the term has defined "gnostic atheist" as the positive claim that there is no god. They may apply a specific definition to their claim of knowledge ("I know to the level of empirical certainty"), but it is still a claim of knowledge.

What, exactly, distinction are you trying to make here?

A "Gnostic Atheist" is someone who lacks belief in a god because they claim to know god does not exist.

So even if I accept your previously stated definition, that is still not a lack of belief. You don't claim knowledge, but you absolutely hold a belief. Holding a belief, even in the negative, is not a lack of a belief.

Yes, it absolutely DOES mean that. You may intend to imply that when you use it, but I certainly don't, and it's nowhere included in the definition.

Only if you redefine "lack" to mean something other than the plain English meaning, which you seem to be doing. Holding a belief in the negative is not lacking a belief

Again, no. If you accept that Gnostic Atheists exist, you cannot simultaneously make this assertion with any level of internal consistency.

Words can have multiple meanings. You know this, so it is weird that you would make such an obviously bad argument.

Atheism at it's most basic means "a lack of belief in a god." It can also take on stronger meanings, when modified with additional descriptors or additional context. You can hold a "mere lack of belief", or any number of more specific beliefs, but all that is directly implied by the word "atheist" lacking some more specific label is a lack of belief-- an agnostic atheist. "I don't know whether a god exists or not, but I lack belief in one."

And for pretty much everyone that lives in a majority English speaking country, people assume the OPPOSITE of what you are suggesting is implied.

Which was already addressed. Use whatever label is most useful for the context.

Finally, don't downvote people just because they politely disagree-- especially if they make a well reasoned argument for their position. It just leads to them downvoting you in return. You are welcome to disagree, but I have clearly stated my position, and justified it WITHOUT redefining plain english words or ignoring obvious truths about the nature of language.