TL;DR, it sounds like agnostic.

I've seen people differentiate between "agnostic atheist" and "gnostic atheist" but I am not sure if those are commonly used terms or just the result of a viral meme about it.

• https://en.wikipedia.org/wiki/Negative_and_positive_atheism
• https://en.wikipedia.org/wiki/Implicit_and_explicit_atheism

Negative atheism, also called weak atheism and soft atheism, is any type of atheism where a person does not believe in the existence of any deities but does not necessarily explicitly assert that there are none. Positive atheism, also called strong atheism and hard atheism, is the form of atheism that additionally asserts that no deities exist.

• Implicit "negative" / "weak" / "soft" atheists who lack a belief in God without explicitly denying the concept, includes very young children, those who are unacquainted with the concept or are truly undecided.
• Explicit "negative" / "weak" / "soft" atheists who do not believe that God exists necessarily.
• Explicit "positive" / "strong" / "hard" atheists who firmly believe that God doesn't exist.

When you say

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.

To me that sounds like negative Atheism. You don't assert there is a divine being. Whether or not that is implicit or explicit is sort of hard to judge based on these statements.

For example, what you are saying is more about how you would react to a god, not necessarily how you'd believe in one. One might argue you're on the fence about Deism. https://en.wikipedia.org/wiki/Deism Because the type of god they believe in is one that is impersonal and does not intervene in their creation. In a sense that's not really contradictory with your statement.

All in all, asserting that the existence of a god would have no effect on how you live your life doesn't really have to do with your potential beliefs in god. For example, someone could believe in the Christian god exclusively but specifically not follow any doctrines they set forth. Perhaps as a means of rebellion or perhaps apathy.

Agnostic fits well. https://en.wikipedia.org/wiki/Agnosticism You say God could exist or not. If you believe it's impossible to prove them that makes you an atheist.

https://plato.stanford.edu/entries/atheism-agnosticism/?ref=whcolony.com#DefiAgno

The terms “agnostic” and “agnosticism” were famously coined in the late nineteenth century by the English biologist, T.H. Huxley. He said that he originally

invented the word “Agnostic” to denote people who, like [himself], confess themselves to be hopelessly ignorant concerning a variety of matters [including of course the matter of God’s existence], about which metaphysicians and theologians, both orthodox and heterodox, dogmatise with the utmost confidence. (1884)