This question about the Eye of Sauron made me wonder about Sauron's true appearance. According to the answers there, the big red eye on top of the tower is partly metaphorical but also a physical thing that exists because of Sauron's evil soul.
There he took up again his great Ring in Barad-dûr, and dwelt there, dark and silent, until he wrought himself a new guise, an image of malice and hatred made visible; and the Eye of Sauron the Terrible few could endure.
The Silmarillion, Akallabeth
During the movies, we never see his true self before he was killed by Isildur. He always has his armor on in the movies. I am not sure if that was because the movie crew were unsure of his true appearance, didn't want to show it, or something else.
Sauron had an attractive physical appearance and offered to help the elves make Rings of Power during the Second Age.
Does he have a true form in the Second Age? Or did he have the ability to change his appearance at will? Which means he might not have one specific form.
I am looking for answers from the books or descriptions by Tolkien.