I came across Sandy Paton's discussion of "Limberjacks" in an old thread called "Kid-mudcateers" Click here If I am not mistaken, one of the references on my GOOGLE search for "Limber Jim" was talking about Limberjacks. If a "Limber Jim" is a dancing wood puppet doing an Appalachian clog dance, then the phrase "be limber, Jim" may refer to a dance, since clogging seems to demand limberness. Once again, there must be some connection with African American dance music here.