I think Apatheist should be taken out. The sheer fact that you said "They may sometimes 'believe' and other times 'not believe' that gods exist, and question whether the issue has ultimate consequences." leads to the notion that they can switch sides and be persuaded in some fashion, which isn't an accurate description of the position.
When someone believes in God, they are a theist. You can't still be an apatheist while still retaining a belief in God, and the inverse is also true. If you have no belief in God, you are an atheist. The amount of time between belief and non-belief is ultimately inconsequential.
It's like being pregnant. At the time of pregnancy, the woman is in fact pregnant. It's a true dichotomy (pregnant, not pregnant). There is no in-between. You either believe in God or you don't. Being uncertain and changing your mind doesn't warrant its own name - nor does it translate in a sliding scale, as it can apply to literally anyone with a brain and a standard of persuasion.
When someone believes in God, they are a theist. You can't still be an apatheist while still retaining a belief in God, and the inverse is also true. If you have no belief in God, you are an atheist. The amount of time between belief and non-belief is ultimately inconsequential.
It's like being pregnant. At the time of pregnancy, the woman is in fact pregnant. It's a true dichotomy (pregnant, not pregnant). There is no in-between. You either believe in God or you don't. Being uncertain and changing your mind doesn't warrant its own name - nor does it translate in a sliding scale, as it can apply to literally anyone with a brain and a standard of persuasion.
My blog: The Usual Rhetoric