[2] After finishing his service, he moved to Boston and then to New York City in the early 1960s, where he worked as a furniture salesman while competing in "talent night" contests against other aspiring entertainers, including Tiny Tim and Barbra Streisand.

[2][10][11] Greer later worked as a floor captain at Arthur, the NYC discothèque opened by Sybil Burton, where he met celebrities such as Margot Fonteyn, Rudolf Nureyev, and Jacqueline Kennedy.

[5] In the fall of 1965, Greer relocated to Los Angeles, where he formed a comedy troupe called "Jack and the Giants" with Roy Gaynor and then-unknown Jim Bailey.

Greer also developed a signature routine that he performed, with variations, for the rest of his career, in which he appeared as the Mona Lisa, speaking through a large picture frame held on his lap and making art-related jokes.

[14] In 1983 he appeared in New York City in an off-off-Broadway revival of Terrence McNally's The Ritz, a farce set in a gay Manhattan bathhouse, starring Warhol superstar Holly Woodlawn.

Greer also directed the Los Angeles production which ran for four months, and appeared on the original cast album (released in 1997 on Moore's Ducy Lee label) as the voice of "the car radio announcer on station KDUL in the Valley.

[9] In an effort to reduce the homophobia of the original script and present a more realistic and positive portrayal of the gay characters, Greer rewrote much of the dialogue and worked with the director.

[17][37][40] The following year Greer co-starred (with Don Johnson) as an underground rock musician in MGM's 1970 box office flop The Magic Garden of Stanley Sweetheart, for which he also co-wrote and sang the song "Water".

[44] Despite the filmmakers' controversial changes to the original stage play, including exploiting the camp and drag-queen elements portrayed by the Queenie character,[45][46][47] Greer's performance received positive reviews[48][49] and has been viewed as a strong statement of gay assertiveness.

[11] Greer aspired to play a diverse range of movie roles, at one point optioning and writing a screenplay about mass murderer Richard Speck in which he hoped to star.

[14][15] Although most media in the late 1960s and early 1970s avoided directly stating that Greer was homosexual (and frequently implied that he was interested in women),[5][9][10] he refused to marry a woman or otherwise pretend to be heterosexual for the sake of his acting career, despite his agent's advice to do so.