Was there a specific geographic area you were interested in? I can really only speak to NYC on this time period.

In the prior decades from the mid 19th Century leading up to WWII in New York open houses of prostitution existed, were well known, and were clustered in specific neighborhoods such as along 8th Ave between 34th to 42nd St or between 125th St to 155th St from 8th Ave to 5th Ave. But the majority of the sex workers in them were women. There is limited evidence for the organized brothel system having boys or men as purveyors of commercial sex during this period. Within the 1920s, partially due to Prohibition, the systems for commercial sex shifted from brothels, saloons, and similar businesses to dance halls and hotel-call girl networks.

This is when we get more evidence of male prostitution, but as part of those loosely organized networks and not as part of open brothels which were sharply in decline. (This is not to say prostitution was in decline, it was not, just that particular model of it was.) George Chauncey describes male sporting culture as conceiving of female prostitutes as interchangeable with male prostitutes, and that this was common knowledge among those within sex work networks so that if a female prostitute was not available at a particular venue a willing gay man might be substituted with no issues from the customer. The evidence of male prostitution grows throughout the WWII period in NYC, but again, in a clandestine more individual manner as opposed to the open manner brothels had operated.

Sources used:

Prostitution and Its Repression in New York City 1900-1931 by Willoughby Cyrus Waterman, 1932.

City of Eros: New York City, Prostitution and the Commercialization of Sex, 1790-1920 by Timothy J. Gilfoyle, 1992.

Gay New York: Gender, Urban Culture, and the Making of the Gay Male World 1890-1940 by George Chauncey, 1994.