A “shade tree barbecue” is an informal barbecue—not always under a shady tree, although that is the image. The Texas term is cited since at least the 1990s. The more well-known term “shade tree mechanic” dates to the 1920s. 5 July 1996, Paris (TX) News, pg. 1, cols. 1-2: That competition was won not by a costumed pair but by look-alikes—a husky bulldog named Gator and owner Jeff Sykes, a member of the Shade Tree Barbecue team. Google Books