Originally Posted by
Drachos
If so, why did he build the Eye?
As B-o-D states, the so-called "Eye of Sauron", or "Lidless Eye" as it is sometimes called, is a psychic projection rather than a physical object. I believe Peter Jackson used the giant electric eye in his films to simplify the story-telling and, perhaps, to make Sauron's physical presence a bit more dramatic.
After Gollum was captured in Mordor, where he had been drawn while searching for the Ring, he was taken to Barad-dûr where he was "questioned and tormented". ('Hunt for the Ring', Unfinished Tales.) Whether Sauron actually lashed him with a whip or turned the crank on a rack is unknown, but seems highly unlikely. Doubtless Sauron interrogated Gollum personally, and doubtless Gollum saw Sauron's physical form as he describes Sauron's Black Hand with four fingers to Frodo and Sam.
Faërie is a perilous land, and in it are pitfalls for the unwary and dungeons for the overbold. – J.R.R. Tolkien, ‘On Fairy-Stories’.