What is Golbez's class? (SPOILERS)

[Chemical]

I think he'd be a Demilunarian or something like that.

That's his race (both him and Cecil)

If you recall their father was lunarian and their mother was human.

But yeah, my educated guess would be that he is a Dark Knight.
I think it would make good game play sense to have it so that he was a Dark Knight while his brother is a Paladin. The whole Ying and Yang - Balance - Good vs Bad - Brother thing.