Elmer (Mousie) Alexander, 66, a jazz drummer who played with Benny Goodman, backed Billie Holiday and played in “The Tonight Show” band before a heart attack curtailed his work. Alexander was raised in Chicago and played in jazz clubs before serving in the Navy during World War II. He moved to New York in 1952 and four years later began an association with Goodman that lasted into the 1970s, during which time he toured much of the world. He performed with Pearl Bailey in a White House appearance for President Richard M. Nixon in 1972. After a 1973 European tour with trumpeter Sy Oliver, Alexander played for two years with Doc Severinson’s band on “The Tonight Show.” He continued studio work after a 1973 heart attack and performed live with the Clark Terry Big Band and the New York Philharmonic. A massive stroke in 1980 interrupted Alexander’s dream of forming his own big band. After his health failed he moved to Orlando, Fla., and in recent years promoted concerts by traditional jazz artists. He also had overcome partial paralysis from the stroke and played for groups of stroke victims. In Orlando, Fla., on Sunday of a heart attack.