According to the Philadelphia Magazine article one of the detectives (Bristow) was in Mexico getting some RR and was still obsessed with the case. He thought maybe no one recognized him because he had been raised as a girl. A street artist in Mexico drew the original BITB as a girl. So, I don't know if it was Frank's idea or just if he was just drawing based on another theory. Bristow died in 1994.
I don't know when Bender drew the BITB as a girl, but Frank Bender was too young to be involved in the initial investigation.
Bill Kelly says the renditions as a girl first a appeared in 1957 and 1958. (Frank would have been only been 15-17 during this time frame)
We see this alot in cold cases. People will start theorizing on something that isn't likely because traditional theories are not yielding results.
Who was the mysterious Boy in the Box? Who killed him, and why? Was his death a tragic accident or a cruel and deliberate act of child homicide? Will this little boy's true identity ever be known, or will he forever remain America's Unknown Child?
americasunknownchild.net
From 2008
Kelly said back in 1957 and 1958, renditions of the child as a girl by a West Coast artist were briefly published in newspaper accounts, but they produced no leads.
He thinks Bender's new rendition may be the clue they've been looking for
Francis Augustus Bender (June 16, 1941 – July 28, 2011) --Oh boy..he shared the same middle name!