Quinn Lemley, an actress and chanteuse, has specialized in portraying Rita Hayworth in a one-woman show—channeling the 1940s glamour queen's songs and mannerisms, sashaying across the stage in elegant evening gowns reminiscent of old Hollywood. But on some mornings after a performance, Ms. Lemley would report to Weill Cornell Medical College for a very different kind of acting job. Her costume for these gigs is two hospital gowns, one wrapped artfully on top of the other, accented by her long, red hair and, on a recent day, four-inch, flaming orange wedge shoes. "I try to wear the gowns in a stylish way," says Lemley, preparing to slip into character as a newspaper editor with severe chest pains and a drug habit. Forget waiting on tables or doing menial jobs. These days, to support themselves between gigs, or simply keep plying their craft, actors are auditioning at hospitals and medical schools to portray sick people—"standardized patients" in med school terms—who help aspiring doctors learn their craft.