ZEN: I remember learning in a behavior course that constant licking provides a feedback from the brain that is pleasurable -- sort of like endorphin release (maybe it was endorphins... it's been a long time ago now)
So sometimes they start for a particular reason, and then just continue because they are bored, it's pleasurable, etc.
I'd have your OTHER dog checked for fleas or mild skin infection -- they will clean each other when there is a problem like yeast / bacteria that you and I may not smell, but they can and want to "fix" it!
Also, have your dog checked for any other medical problems. It is a very unusual presentation of medical disorders, but good to have full checkup and blood-work screen done if you can.
I totally second the KONG .. it is an amazing treat dispenser... I stuff them with peanut butter or canned food (or a mix). Also you can stuff dry treats in there. They will spend a lot of time working to get these out.
One warning... my dog is too smart. She learned that if she tosses the Kong the goodies come out easier -- she almost broke our window by throwing the Kong at it. No more Kong for her!
Just interrupting the behavior ("NO"), and then rewarding your dog with a new item to pay attention to. Increased exercise if they aren't getting enough daily. Increased brain activity of any kind.
Pretty amazing to watch, though! If your other dog doesn't have skin problems yet, it will!
Good Luck.
Jes



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