Kav ha-Yashar says one should guard their eyes, that's important, though guarding your tongue, is most important. Why? Because your eyes only protects your soul, while guarding your mouth is guarding two souls, your soul and that of your brothers and sisters.
I recall a shiure, they mentioned a certain Kabbalist (It may be Rabbi shimon baryochay) who asked why we don't have two mouths, one for learning and one for talking / eating, he was answered with something along the lines of, one does enough damage, or, can you control just one mouth.
That is all great,
Though the great rabbis and or Mystics will easily promote guarding the eyes over your mouth. The question is why, why are they more concerned with the eyes than the mouth. Looking at Baba Elazzar Abuchatzera, who had a tunnel just to protect his eyes, and he's just one from the many in his family and the families alike.
You don't see them doing ta-anit dibure none stop, or anything of the like, so what is going on? Which is the real deal, guarding your eyes or your mouth.