It is a derivative of fagot. A gay person who acts like a fagot or an act of being gay.

Also commonly spelled Fagoty
You know Charles, you may be gay but you really act fagotty around Justin. I think he may be your soulmate.

Quit acting fagotty!
by MarksOneAndOnly! November 4, 2010
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(Bassoon) traditional name for a woodwind instrument in the double reed family
I play the fagotti in the school orchestra
by MissRuss November 14, 2014
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