Off Broadway longrunner “Naked Boys Singing” will throw in the towel at the end of the month after a 12 1/2-year run.Show managed a long commercial life in an Off Broadway climate where many producers feel for-profit stage productions have become less and less viable as costs rise and marketing campaigns are eclipsed by Rialto offerings. When it closes on Jan. 28, the musical will have played 3,069 perfs since it opened at the Actors Playhouse in 1999 before shifting to Theater Four in 2004 and then to New World Stages in 2005. “Naked Boys Singing” was boosted in part by the goofy novelty title that attracted the attention of tourist auds, often the hardest demo for Off Broadway to capture. Production also appealed to group auds, including bachelorette parties, while adjusting its performance sked to match demand. Currently, the tuner plays just two perfs per week. Productions of the show also have played cities including Las Vegas and Los Angeles as well as London, where a production is currently on the boards. An upcoming incarnation is planned for Sydney. Show was conceived by Robert Schrock, who teamed with a dozen scribes (including Bruce Vilanch) to pen the revue. Jamie Cesa, Carl D. White, Hugh Hayes and Tom Smedes produce.