This song is a good choice! You can definitely see how it follows Macbeth’s story. The speakers in the song basically suggest that through their rise and fall the person in the mirror, the self, is the only one there to stand by them.
Consider these lines in the opening stanza.
I see the blood in your eyes
I see the love in disguise
I see the pain hidden in your pride
I see you're not satisfied
And I don't see nobody else
This reminds me of the fact that Macbeth is hiding his anger from Duncan when he finds out that he is not named Ducan’s successor to be king in Act 1, Scene 4. The song mentions rise and fall, it is defnitely about ambition.
[Aside.] The Prince of Cumberland! That is a step(55)
On which I must fall down, or else o'erleap,
For in my way it lies. Stars, hide your fires;
Let not light see my black and deep desires:
The eye wink at the hand; yet let that be
Which the eye fears, when it is done, to see.(60) (enotes etext pdf p. 18)
He is pretty much echoing the lines in the song, that he knows what is in his heart but others do not.
At the end, Macbeth might relate to these lines from the song.
Mirror on the wall, here we are again
Through my rise and fall
You've been my only friend
You told me that they can understand the man I am
So why are we here talkin' to each other again?
In Act 5, Scene 5, Macbeth resigns to the fact that he is alone. Everything is coming down on him. Ambition leaves you alone.
She should have died hereafter;
There would have been a time for such a word.(20)
Tomorrow, and tomorrow, and tomorrow
Creeps in this petty pace from day to day
To the last syllable of recorded time;
And all our yesterdays have lighted fools
The way to dusty death. Out, out, brief candle!(25)
Life's but a walking shadow, a poor player
That struts and frets his hour upon the stage
And then is heard no more. It is a tale
Told by an idiot, full of sound and fury,
Signifying nothing.(30) (p. 84)
When the speaker of the song suggests that the mirror has been his only friend, Macbeth also ends up alone and doomed.