A gayden is the gender inverse equivalent to a transbian. It refers to androphilic trans men who only have an interest in dating other gay men. It is a play on the name "ayden," which trans men stereotypically name themselves post-transition.
Gaydens were typically either fruit flies or fujoshis prior to transition and have always had a strong affinity for gay men.
Guy#1: Don't call him by his dead name anymore, he's a gayden now. He transitioned and only dates men.
Two gay pining characters from some sort of media. The trope is generally associated with friends/enemies/lovers. Some examples include:
Keith and Lance (Voltron: Legendary Defender)
Adora and Catra (She-Ra and the Princesses of Power)
Asami and Korra (The Legend of Korra)
Ruby and Sapphire (Steven Universe)
Tony Stark and Steve Rogers (Marvel Cinematic Multiverse)
Ash and Gary (Pokemon)
Light and L (Death Note)
Sweater gays are gay men and women who are largely non-threatening to heterosexual people because their lifestyles largely emulate the heterosexual ideal. They often live in the suburbs and usually have children.