I’m curious if there’s a name to the belief I have. I wouldn’t exactly call it atheist, though i generally lean that way, but I wouldn’t call it non-theist. The thing is, I just plain don’t care if God exists or not. They could, or they couldn’t, it really has no bearing on how I live my life. For that reason along I think I go in the atheist camp, but I always thought that was used to describe people who don’t think he exists.
Say you have a jar full of jellybeans. We know that the number of whole jellybeans in the jar must be either even or odd.
If someone asks you if you believe the number of jellybeans in the jar is even, you can and should say “no” if you haven’t counted them or otherwise gathered any evidence to support that conclusion. To believe something is to say you feel it is more likely true than false, and you can’t say that about the given proposition.
Importantly, this does not mean you do believe the number of jellybeans is odd. The fact that one of those two things must be true does not mean you have to pick one to believe and one to disbelieve. It is perfectly rational to reserve belief either way until you have evidence one way or the other. You do not believe it’s even, nor do you believe it’s odd.
So, if we define “atheist” as “someone who does not believe in any gods”, I think you meet the definition of atheist. Just like the person in the above example does not believe the jellybeans are even & also does not believe they are odd, you don’t need to believe “there are no gods anywhere” to not believe “there is at least one god”.