I always get confused when I come across a new term because the word has settled somehow not knowing how it did…Who started the fire? At any rate, in the song 愛しの彼が振り向かない[itoshi no kare ga furimukanai] Mikuru version, there is a line saying,
腐女子が味方のガチホモいるけど ノンケの彼には意味が無い[fusjoshi ga mikata no gachihomo irukedo nonke no kare niwa imi ga nai]
Yes, it mentions Koizumi and Kyon in the Melancholy of Suzumiya Haruhi. I could translate like “there is a deep gay who has a lot of fujoshi followers, but it doesn’t work for the straight him.” I know ホモ means homo, but what does ガチ[gachi] mean? Actually this is not my first time seeing ガチホモ, but I have encountered a couple of times when I heard of any doujin works. Mostly, it says like ○○はガチホモ [xxx wa gachihomo]…I am pretty sure this ガチmakes something stronger or harder. Don’t believe my assumption too much, but maybe I am right. I guess this ガチorigins from ガチガチ[gachigachi] which means very hard, or as hard as a stone. Oh, can I say a hard gay to put it? So ガチホモ could be abbriviation of ガチガチのホモ[gachigachi no homo]. Incidentally, ノンケ[nonke] means straight. Though ケ should be written in katakana here, it should be 気[ke] in kanji. ノン is non-, so this 気 stands for the homosexual orientation. To say directly more, you can say ホモっ気[homokke]. 彼はホモっ気がある[kare wa homokke ga aru] means he seems to be gay.
Having said that, I believe fujoshi would like to point out the character seems to be gay even in the original work when they say ガチホモ. Yes, Koizumi sometimes gets near Kyon too much when he speaks to him(and Kyon says it’s too close, man!). It really faciliates BL fangirls to make Koizumi×Kyon pairing. Speaking of a ガチホモ, I can think of Koizumi, Nagisa Kaoru[Evangelion], Gunter[Kyou kara maou], and Lord Dio Eraclea[Last Exile]←(this is what a friend of mine said, not me).
Thanks to ガチホモ characters, BL doujin girls can make a pairing so easily. If you happen to be a fujoshi and try to make a BL fan-made comic, find a ガチホモ guy, so it would make it easier for you.