[The Squatter of Amon Rûdh]

Everything there is to know about the Mouth of Sauron for the purposes of this thread is in The Return of the King. The following passage from The Black Gate Opens ought to make the whole situation painfully clear.

The rider was robed all in black, and black was his lofty helm; yet this was no Ringwraith but a living man, The Lieutenant of the Tower of Barad-dûr he was, and his name is remembered in no tale; for he himself had forgotten it, and he said: 'I am the Mouth of Sauron.' But it is told that he was a renegade, who came of the race of those that are named the Black Númenoreans; for they established their dwellings in Middle-earth during the years of Sauron's domination, and they worshipped him, being enamoured of evil knowledge. And he entered the service of the Dark Tower when it first rose again, and because of his cunning he grew ever higher in the Lord's favour; and he learned great sorcery, and knew much of the mind of Sauron; and he was more cruel than any orc.

When cross-referenced with the Tale of Years, this passage gives us a rough age for the Mouth of Sauron: he must have been alive before 2951 TA, when Sauron began rebuilding the Dark Tower and declared himself openly again; and since he learned no sorcery before then, he must have been born not long earlier. It also states quite categorically the common belief that he was a Black Númenorean. It doesn't say that he was one, but this is an instance where Tolkien remembered that he was trying to write his story as a chronicle. He couldn't give the story of the Mouth of Sauron as the narrator without some sort of logical source for the knowledge. Anything not contained in this one chapter from The Lord of the Rings is speculative and cannot be confirmed, unless for some reason references to the Mouth were overlooked when making the index to the History of Middle-earth, in which I can find no reference to him.