Here is the location of the left hand arm rest on a 1937 Ford De Luxe Fordor. I don't have one on the right. Not sure if my car had been originally equipped with one on the right or if it had been removed by someone during the intervening years.
you would think a De Luxe would have an arm rest on both sides. Maybe that was for those snooty Lincoln drivers and their fancy arm rests on both sides.