The person that fits most of the ones that I thought of is Saruman.
Faithful I, - the flaw in this guess
yet I my lord betrayed - well, he did. He betrayed Eru.
To serve the one who wielded shadow; - aka Sauron
Shadow I helped defeat. - well, half of TTT is about Saruman's double treachery.
Patient was I, but rash move I made. - in "The Voice of Saruman", he begins as a patient but slightly annoyed superior, but then he looses control over himself
Madness tore me; - don't you think he
was a bit mad when he met Frodo&others on their way to Rivendell, and even madder in The Scouring of the Shire?
now at last I Know what it is to sleep. - ieI DIED
Doesn't really fit, but fits more than other traitors that I considered. I have the feeling that the real answer is pretty obvious, and its laughing at me right now
