Born in Los Angeles, California, Abascal started his career as hair stylist in the early '80s and worked on the thriller The Osterman Weekend (1983, starring Chris Sarandon and Meg Foster), the television drama My Mother's Secret Life (1984, with make-up artist James Kail), the thriller Thief of Hearts (1984), the family drama Sylvester (1985), Joe Dante's science fiction adventure Explorers (1985, with James Cromwell, Brooke Bundy, Robert Picardo, Dick Miller, Frank Welker, and make-up artist Zoltan Elek), the romance Pretty in Pink (1986), the comedy Ferris Bueller's Day Off (1986, with Alan Ruck), the action thriller Opposing Force (1986), Richard Donner's action film Lethal Weapon (1987), and the television film Cameo by Night (1987, with David Graf).