You may be confusing Searchlight with Pahrump.
Prostitution is ILLEGAL in Searchlight and there are no brothels there. In fact, prostitution is ILLEGAL all over Clark County (but certain aspects of the trade are underenforced in Vegas).
Pahrump, however, DOES have legal brothels. But Pahrump is in Nye County, and that county allows it (though it is heavily regulated, naturally).
Were things different in the past? Possibly. But that's where it stands now.
It’s been a long time since I was in that part of the country, but I remember my Dad and some of my uncles telling me tales of what went on in Searchlight. Whether it was legal or not, I don’t know.