While wandering in San Francisco, Oedipa gets swept into a gay bar called The Greek Way where she meets a man with acne and large ears. He is wearing a pin on his lapel, and on it is the symbol of the muted post horn. When she questions the dude, he tells her that he is a member of Inamorati Anonymous, a group to help people kick the addiction to love, "the worst addiction of all" (5.64).
The man tells Oedipa an elaborate story about their founder, a Yoyodyne executive who decided to kill himself when he was replaced by an IBM computer, but later changed his mind.
This big-eared guy then wanders off to the bathroom and never returns. Later in the novel, Oedipa calls the bar from a payphone and asks to speak to the man. At this point, she is desperate and possibly suicidal. She begs the Inamorati member to tell her what is going on. He tells her it is too late. Not for her, but "For me" (6.143).
Even though he's a minor character, the Inamorati Member is one of the few men in the book with whom Oedipa has a real connection. It is clear that Oedipa herself suffers not from an addiction to love, but from a lack of it, and it is sad and ironic that the only man she can reach out to in the end is one viciously opposed to the very idea of love.
It's also worth noting that Pynchon gives us all sorts of reasons the man could have given up on love. For example, he is described as not being very attractive (poor dude) and Oedipa finds him in a gay bar, which might suggest that he is not opposed to love as such, but that he's gay—the 1960s were insanely hard for the LGBTQ community.
Lastly, it's worth noting that the member is one of only a few characters who escapes without a name… which in a Pynchon novel might be equated with some small dignity.