Green’s Dictionary of Slang

(gay) an obviously, exaggeratedly homosexual man; thus brilli adj., effeminately sentimental.

1941		G. Legman ‘Lang. of Homosexuality’ Appendix VII in Henry Sex Variants.
1947		(con. 1944) J.H. Burns Gallery (1948) 127: At closing time in her bar, some of her boys, a bit brilli, would cry on her shoulder and tell her that she was just like some elderly lady in Arkansas.
1965		Guild Dict. Homosexual Terms 5: brilliant (n., adj.): Active and successful homosexual male.