Actually, gnostic and ignostic atheism can also both be tenable positions.

Here's how: Specific conceptions of deities that have actually been elaborated upon in the theological and apologetic literature can be shown to (pretty much universally) contain logically inconsistent characterizations.... in effect talking about something like a "round square". A description that is logically inconsistent cannot refer to any real thing. So in the same way we know that a "round square" cannot exist, we can know that conception of a deity that is logically inconsistent cannot have a real referent.

It's like the pink unicorn that's always invisible... from the concepts involved and the way they are related, it logically follows that this characterization cannot refer to anything.

So, gnostic atheism is possible for specific conceptions of god. Every specific elaboration I have come upon in my 16 years of academic study has involved such conceptual inconsistencies.

But since very specific claims are made about deities (specifically, what things in the observable world they are responsible for), we actually need a fully fleshed-out model to 'do the legwork' of showing how the general idea might make sense (in light) of the available facts.

The general idea of theism (and deism) cannot do this by itself - it isn't 'susbtantial' enough to be evaluated as 'true' or 'false'. But that doesn't get us to agnosticism, rather it gets us to 'ignosticism' - the position that the concept of a deity is too ill-defined to be evaluable.

There's also the approach from epistemology: It can be argued that the theistic hypothesis (as well as the deistic hypothesis) could not possibly explain anything, because it cannot - by its very nature - provide any sort of description of how the things it is supposed to explain came about. But something can explain (and thus, potentially predict) only when it gives us a working model of how the explanadum phenomenon came to be realized. Merely citing a supposedly responsible, 'supernatural' agent cannot be explanatory. Since theories gain epistemic probability solely by providing explanatory (and predictive) power, nothing can ever actually count in favor of theism.

Thus it's possible to (rationally) entertain gnostic atheism about specific conceptions of deities (like the characterizations by Aquinas, Swinburne, Plantinga et al.), while entertaining an ignostic atheism towards the general idea of deities.

[Sources: MPhil-degree in Formal Logic, Philosophy and Philosophy of Science. For the logical inconsistencies of fleshed-out characterizations of deities, see: Mackie, J.L., The Miracle of Theism; Sobel, J.H. Logic and Theism: Arguments for and against Beliefs in God ]