Since people seemed to like my post on the American Crusader, I thought I'd post another Thrilling Comics character that I like and has been reinvented several times, The Woman In Red.
The Woman In Red is actually credited as the first female masked crime fighter, beating out Wonder Woman, Mary Marvel, and Phantom Lady, and herself was only beaten as first female superhero by one month by Fantomah. Though she never made a cover appearance, she was a regular feature in Thrilling Comics starting issue #2, with her last appearance in issue #46.
Her real identity was Peggy Allen, a policewoman who was frustrated by the limits of her job and created a secret identity. She was aided by the police commissioner, who considered her his operative, and informed her of strange cases, arranged for her undercover investigations, and occasionally kept the regular cops out of the way, who were unaware that they had a vigilante on their payroll.
Peggy's gender almost never came up, outside of some of her disguises and taunts by villains. The joke made in the last panel of this story is the most I can really think of - well, that and occasionally showing her legs.
Warning for racism.( Thrilling Comics #5 )