Apathetic agnosticism is not knowing if any gods exist or not and also not caring if any gods exist or not. Agnosticism by itself only deals with knowledge and doesn’t imply whether an agnostic cares about the existence of gods or not.
So, what is the definition of agnosticism? Some imagine that agnosticism is an alternative to atheism, but those people have typically bought into the mistaken notion of the single, narrow definition of atheism. Strictly speaking, agnosticism is about knowledge, and knowledge is a related but separate issue from belief, the domain of theism and atheism.
"A" means "without" and "gnosis" means "knowledge." Hence, agnostic: without knowledge, but specifically without knowledge of gods. It may be technically correct, but rare, to use the word in reference to any other knowledge as well, for example: "I am agnostic about whether O.J. Simpson actually killed his ex-wife."
Despite such possible usages, it remains the case that the term agnosticism is used fairly exclusively with respect to a single issue: do any gods exist or not? Those who disclaim any such knowledge or even that any such knowledge is possible are properly labeled agnostics. Everyone who claims that such knowledge is possible or that they have such knowledge might be called "gnostics" (note the lowercase 'g').
Here "gnostics" is not referring to the religious system known as Gnosticism, but rather the sort of person who claims to have knowledge about the existence of gods. Because such confusion may come easily and because there is generally little call for such a label, it is unlikely that you will ever see it used; it is only presented here as a contrast to help explain agnosticism.
Confusion about agnosticism commonly arises when people assume that "agnosticism" actually just means that a person is undecided about whether or not a god exists, and also that "atheism" is limited to "strong atheism" – the assertion that no gods do or can exist. If those assumptions were true, then it would be accurate to conclude that agnosticism is some sort of "third way" between atheism and theism. However, those assumptions are not true. Commenting on this situation, Gordon Stein wrote in his essay "The Meaning of Atheism and Agnosticism":
Obviously, if theism is a belief in a God and atheism is a lack of a belief in a God, no third position or middle ground is possible. A person can either believe or not believe in a God. Therefore, our previous definition of atheism has made an impossibility out of the common usage of agnosticism to mean "neither affirming nor denying a belief in God." Actually, this is no great loss, because the dictionary definition of agnostic is still again different from Huxley's definition. The literal meaning of agnostic is one who holds that some aspect of reality is unknowable. Therefore, an agnostic is not simply someone who suspends judgment on an issue, but rather one who suspends judgment because he feels that the subject is unknowable and therefore no judgment can be made. It is possible, therefore, for someone not to believe in a God (as Huxley did not) and yet still suspend judgment (ie, be an agnostic) about whether it is possible to obtain knowledge of a God. Such a person would be an atheistic agnostic. It is also possible to believe in the existence of a force behind the universe, but to hold (as did Herbert Spencer) that any knowledge of that force was unobtainable. Such a person would be a theistic agnostic.