We have a 5yr old rescue SBT who is mouthing very badly.  The first week with us it wasn't too bad, just mouthed excitedly when petting him, now he's jumping and mouthing hands, our faces when bending down and even when snuggling into us.  I don't believe it's aggression, more exuberance, we are sharply saying AHH AHH and he stops immediately but while he is learning amazing fast in every other respect there is no progress with this at all.

This is our first SBT so not sure if it is a breed, rescue or just his individual issue.  I need advice on how to deal with this please as he is otherwise an absolutely brilliant, obedient and loving dog.

How hard is he mouthing?

Well it's not really hard snapping or biting, just closes his mouth on you and opens immediately again. Not painful for us in the least but worrying as more of a behaviour issue, we won't like it done with a stranger who doesn't know that otherwise he is lovely!