To be precise about my question: are there any pairs of signs in ASL or other sign languages where mouthing different words is the only thing which distinguishes two signs from one another? I’m asking primarily about ASL, but if there are other sign languages to compare to or contrast with, I am also curious.
One example is the fact that
ex are signed the same. So you can distinguish the two by actually mouthing the English word.
Another example is that for example
write carelessly and
write carefully are distinguished by mouthing. To say "carelessy", you can whisper "thhhh" as you tilt your head toward your dominant arm. To say "carefully" you can show the tip of your tongue between your lips (as if to pronounce "L") as you tilt your head toward your non-dominant arm.
I think it's worth pointing out that the entire face and even head are involved in enunciating the morpheme that means "carelessly" or "carefully". I think it's analogous to how a phonemic contrast in a spoken language might involve both vowel length and vowel quality, even if we call it "the short vowels and the long vowels".