#2 who is on the fence lacks the belief that there is a deity. But #2 is not an atheist.
There is no such thing as "the best usage being what an atheist chooses to describe himself". Atheist is a label to describe somebody with a particular belief. It is not some default person claiming he is atheist, and then choosing a description for himself. Anybody can call themselves whatever the hell they want. That is not the point. The point is historical standard usage.
In the workings of knowldege, there is something called the threshold of certainty. It is beyond this threshold, that somebody has come to the conclusion on a matter. X is true. Thus, the person states "I know X is true" when he has gone beyond a threshold of certainty in a matter. Does this mean that the person is going to bet his testicles on it in a gamble? Not necessarily.
So I might conclude that I have an apple in my hand. I can say I have passed the threshold of certainty, and know I definitely have an apple in my hand. If there is no apple in my hand, one must prove me otherwise.
The term atheism, by standard, describes people who, at whatever level of certainty they may be, are claiming that there is no God. In such as case, they live as if there was no diety unless proven otherwise. This is an atheist.
One who simply lacks the belief in a deity could be an atheist as described above, but isn't necessarily one. Because those who state they don't know either way lack the belief, but aren't actually atheists. Typically, they may incorrectly be referred to as agnostics. Those who abide by infidel's terminology label them as weak atheists. The real question is, why, if you aren't actually an atheist according to standard usage of the term, would somebody in this case even want to refer to themselves as an atheist? It's as pointless as wanting to refer to yourself as a theist.
So what happens when somebody claims that they don't know whether or not there is a diety, but are pretty sure there isn't one? The answer is that it doesn't matter. The real question is where do they stand on their threshold of certainty?
1. Are they at a level of certainty where they pretty much consider the universe to be without any diety? Then they are atheist.
2. Or are they at a level where they really don't know either way. Then, they aren't atheist, and should have no reason to even want to be called one. Nor should we take people seriously who want to group them under atheism using poorly concocted terms such as "weak-atheism" and "strong-atheism". And even going further as to proclaim agnostics as a type of atheist.
When you call yourself an atheist, you're basically telling the public that you believe there is no diety. You may not necessarily bet your left testicle on it. But that's how you live your life. No God. No religion. Atheist.