Personally I think Sauron had no second in command just like Morgoth did not (Morgoth had Gothmog, Sauron, Glaurung as commanders/lieutenants) who was a TYRANT, but rather his own most trusted servants. And since Maia (or in the case of Morgoth Vala) tended to be immortal and very powerful, they probably did not perceive the thought of their own downfall, thus ruling out the need of a second in command.
What is the point of a second in command in Mordor (by that I mean where his power runs) if the ruler dies whose power is what keeps the entire realm sustained. You must understand that under Sauron's dominion the Mouth must also have been under his will, doing whatever he bids. So the Mouth really has no greater authority than the rest of Sauron's following. For example, the Mouth could not have commanded the Nazgul because they followed the will of Sauron alone. Nor could the Nazgul or even the Witck king command the Mouth because he was too, under the direct control of Sauron.
Its not as if the Mouth would have got first dibs on commanding the Ringwraiths if Sauron took a holiday or something because it was just not possible. Sauron could have had the Lord of Morgul, Lord of Isengard, Lord of wherever the hell he wants, but ultimately they were all his servants.
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