From the record
“The Bearwallow Mountain Lookout Cabins and Shed are located in the Bearwallow Park near Mogollon, New Mexico. Built in 1940 by the Works Progress Administration, they are one of three New Deal-era buildings in the Gila National Forest, which also include the El Caso Lookout Complex and the Mangas Mountain Lookout Complex.”
Wikipedia article Bearwallow Mountain Lookout Cabins and Shed, CC BY-SA 4.0.
One of 7 National Register listings published here for Catron County · listed in 1988 · category: Building · built in 1923.
Sources: the Wikipedia article · the case file at the National Archives · the National Register database, National Park Service