An ineffaline gender is a gender that defies all forms of classification. Any label or attempt to classify the gender with human language will be rejected. An ineffaline gender will say "no, I'm not masc, fem, or neutral" and "no, I'm not atriary either" and "no I'm not xenic or outherine" and it will continue like this. An ineffaline gender in not masculine, feminine, neutral, outherine, xenic, or anything related to any of them. It is also not related to any terms that may be coined in the future. For as long as people come up with new terms an ineffaline gender will reject those terms. It is not necessarily because the person who possesses the gender is questioning or doesn't understand their gender. An ineffaline person can be strongly gendered, and fully confident in their gender, but all labels or descriptions that exist don't seem to fit.
Basically, ineffaline is the "everything else" category. If you are not ineffaline, that means, by definition, you must identify with an existing gender term.
Ineffaline is a description of gender (in the same way masculine, feminine, androgynous, outherine, etc, are used) It's based on the word ineffable. The adverb form is ineffity or ineffalinity.
Admittedly, due to the definition of ineffaline, and ineffaline person is probably going to reject the label of ineffaline on principle, so I don't know how useful with term actually is.