Drake had migrated from Oklahoma to Dallas, TX to perform in regional theater after graduating from college. While he found regular work, he was unable to land a local TV commercial and decided to return to school. Auditioning for a university program towards a doctorate in theater, Drake was advised to abandon his plans for a teaching career and try his hand as a professional actor. Emboldened, he relocated to Southern California in 1980 and soon found employment at San Diego's Old Globe Theatre where he worked for four years. On occasion, Drake was able to snag small roles such as in the 1981 CBS movie "Dark Night of the Scarecrow", or in the feature "The Karate Kid" (1984).
In 1987, Drake auditioned for a one-scene role on an episode of "L.A. Law"; the role was as a mentally-impaired adult male who had unwittingly committed a crime. Audience reaction to the character was so favorable that he was asked to join the regular cast of the series. His character, Benny Stulwicz, held a job at the law firm, learned to live on his own, found romance, tried to adopt a homeless teenaged boy, and provided an oddly common sense take on some of the more bizarre events at the firm. After winning his first Emmy, Drake landed strong supporting roles in TV-movies, including "Too Good to Be True" (NBC, 1988), a remake of the 1945 feature "Leave Her to Heaven", and "Murder in New Hampshire: The Pamela Smart Story" (CBS, 1991). By the late 90s, he had a pivotal role in the NBC miniseries "Peter Benchley's 'The Beast'" (1996) and returned to the series grind as co-star of the ABC drama "Prey" (1998).
Trying to capitalize on his small screen fame, Drake segued to features as the deliciously sadistic crime boss Robert G Durant, the nemesis of Liam Neeson's "Darkman" (1990), a role he reprised in the Neeson-less sequel "Darkman II: The Return of Durant" (1995). He also portrayed a murderous heart surgeon in "Dr. Giggles" (1992) and a wealthy plantation owner searching for a runaway female slave in 'The Journey of August King" (1995).