Re Electric cars-
Obviously the original Brady didn't arrive in an electric car. The shooting occurred in 1880. The first (3 wheel) electric car was made in France in 1881, followed by London (1882) Boston (1888) and Iowa (1890). (Encyclopaedia Britannica 1985)

    Somebody suggested this as a confusion with Diamond Jim Brady who is primarily famous for two things- his enormous meals and for being the first person in New York City to own an automobile (in 1895). Nice quote-

"To Long Branch, the gambler Diamond Jim Brady brought Lillian Russel. Brady designed and commissioned an electric car with a rounded glass front, with no headlights but a hundred bulbs in that transparent interior, where the couple could seat themselves on display, two large-bodied people adorned with brocades and sparkling jewelry, gliding silently at dusk down the oceanfront promenade, trailed by a procession of spare cars, each chauffeured and ready to serve in case of mechanical failure."
Thousands of Broadways: dreams and nightmares of the American small town By Robert Pinsky

    There is another possible confusion, however- not mentioned above- with Charles Brady King- who was an engineer, artist, mystic and inventor.   King test drove his (not electric) first car in Detroit on March 6, 1896, at speeds up to seven miles per hour. King provided parts, instructions and assistance to Henry Ford for his first car. This would explain why James Brady is called "King" Brady in the song.