---- In other words, can you make additional assumptions about atheists, beyond "does not have a belief that a god exists"? I think it would be very hard to do so -----
I do not think so. First the sentence above is tricky. Does it mean that atheist has no belief whatsover on the subject of god's existence? In that case, a rain drop is an atheist. Then this definition is faulty -- I think, a raindrop is not in a position to form a view on any issue. Definition of atheism as merely "absence of theism" or mere "lack of belief in deity", tries to impose only a particular variety of atheism as true "atheism".
OTOH, if, we take the definition to imply that atheists have weighed various reasons for not believing in any deity then It means that atheist holds a conscious position regarding non-existence of deity, irrespective of actual existence or non-existence of a deity. The unattainability of knowledge for or against the existence of gods can be seen as indication that atheism requires a belief.
In the second understanding of the given definition, It was shown that in common usage "I do not believe that the letter was delivered" means "I believe the letter was not delivered".