Every time I see this meme question I realize that non binary terminology is very new.
Terms like genderqueer and androgyne (which I also identify with) existed back then, and around 2003-2005 I was all over now long dead websites researching it.
IIRC genderqueer is 70s or 80s vintage and androgyne in this context is noted in the late 1800s.
But I didn't encounter the term 'non binary' until much later.
When did non binary become a term anyway?
I guess I'd say "research androgyne gender" or something.
There was also "neutrois" (since 1995.) I identified that way for a while; I didn't know how to pronounce it, but that's never stopped me before.
As for the question itself, a bit of Google Books spelunking identifies a few stages:
In the 1990s when people (anthropologists, language theorists, Kate Bornstein) used "nonbinary" to talk about gender, they usually meant something like "non-binarist" by it -- the term was applied to systems, and ways of thinking and acting.
There were a couple of exceptions from at least back to 1991 (Ehrlich et al.) and increasingly more through the 2000s, where "nonbinary" is an adjective used to describe identities rather than systems (so summarizing genderqueer, androgyne, etc - but still not an identity in its own right.) A notable subset of these are multiple works about MUDs from the mid-2000s resorting to this term to summarize the 10% or so of MUD users who identified outside the binary.
It's not until the very early 2010s, and definitely by 2012, that "nonbinary person"/"nonbinary people" is firmly established as a term, so basically the modern usage.
("Enby" was very definitely coined by someone on tumblr in September 2013 and exploded onto the internet very quickly after that; I combed through all the twitter results before that date for "enby" and they were all typos)
