In SW New Mexico, JWJ was alleged to have spent time in Hillsboro, Steeple Rock and Silver City, where it's said he was the silent owner of the old Southern Hotel, which was destroyed in a flood in the early 20th century. We've located a similar mirrored JJ 'anchor' (rounded, not squared style) - I'll post it if I can locate the pic. The other carving (the zigzag) seems appropriate to the JWJ topic too.
Now that JWJ has entered the conversation, then yes, old mines can possibly be important. For example, what better place to hide something than in an empty hole? Good luck and good hunting.