Palmer attended Watchung Hills Regional High School. His first band was the Myddle Class, formed in 1964 under the initial name The King Bees while members were still in high school. As the Myddle Class, the band performed at such clubs as the Night Owl in Greenwich Village, and released several 45s on the Tomorrow Records imprint before disbanding in 1969. Palmer next formed the Quinaimes Band with several Myddle Class members, which recorded an album for Elektra Records before disbanding shortly thereafter.
At the insistence of ABC Records executives, Palmer joined Steely Dan in an early incarnation in 1972. He sang lead on two tracks on their debut album, Can't Buy A Thrill – "Dirty Work" and "Brooklyn (Owes the Charmer Under Me)" – as well as doubling parts of Donald Fagen's vocals on "Reelin' in the Years", "Only a Fool Would Say That", and "Change of the Guard" to reach the high notes. He also sang lead on most of Steely Dan's songs when performed live in their early concerts as a result of Fagen's lack of live vocal power at this point. Fagen eventually took over as lead vocalist and Palmer left the band, but Palmer did contribute backing vocals on the band's subsequent release, Countdown to Ecstasy.
After his exit from Steely Dan, Palmer worked with a number of songwriters, including Carole King in the composition of "Jazzman". He later formed the band Wha-Koo with Danny Douma. Wha-Koo released three albums, "The Big Wha-Koo" in 1977, "Berkshire" in 1978 and "Fragile Line" in 1979. He also contributed the song "Silhouette" to the 1985 film Teen Wolf. The song plays during the house party sequence where Scott and Boof participate in Styles' "games."