For the human character, there's the whole QUILTBAG spectrum. I'm not sure exactly what you mean by gender neutral in this case. Intersex, asexual, transgender, transsexual, gender-fluid/genderqueer, third gender?
For an intersex character, there's Laura Lam's
Pantomime. She's actually a Chronner, although hasn't been here much. There are asexual characters out there, and plenty who don't conform to the 'standard'* gender roles.
Careful!
Ask three people for their definition of anything, and you'll get three answers! There's a spectrum of sexuality and, more importantly, personalities. Everyone's different.
Good luck with your writing.
*Standard not always being the same, depending upon time and location.