I'm taking a guess that Dean Wareham most likely came to Time by Nancy Sinatra's version... I know I did. All my (admittedly rather slack) research has revealed that Time songwriter Michael Merchant wrote Time. And that's about it. A few folk recorded in 1966, including...
Time - Nancy Sinatra (1966)
Time - Cher (1966)
Time - Carol Deene (1967)
Time - Glen Campbell (1969)
Dean Wareham's side project Cagney and Lacee recorded the sonmg for a single on Terry Tolkin's No.6 Records in 1995
MP3: Time - Cagney and Lacee (1995)