what were The Silent Watchers?

[Legate of Amon Lanc]

I think, however, that there were more than two Silent Watchers - I suppose at least two more were in Minas Morgul:

"Bad business," said Gorbag. "See here - our Silent Watchers were uneasy more than two days ago."

As we know, Gorbag was leader in Minas Morgul. These are not Shagrat's Silent Watchers from Cirith Ungol we are speaking about here.
So if the Blue Wizards were to become Silent Watchers (which I find unlikely, supported even by the evidence stated in posts above), we would need two more unknown Wizards to occupy the posts in Minas Morgul.

I am more inclined to think about the "spirits", maybe even as hwaim said even trapped spirits of someone... but if you gave me the choice, I'd most likely side with Squatter:

Originally Posted by The Squatter of Amon Rûdh

That being said, though, I think that the Watchers are more effective in their narrative context for their inscrutability. The fact of their malicious will is enough for me: I don't need to know how it got there, and the feeling of the unknown that they evoke adds to their menace. That may even be why Tolkien left them unexplained.