I made sure to write them down, and while listening to the recording again to verify them, I noticed a connection between the chords and the lyrics.
The chords for the verses, as I figured them out, are:
C minor | Bb major | Eb major | C minor
Eb major | F major | C minor
C minor | Bb major | Eb major | C minor
Eb major | F major | C minor
Each line in the verses contains both a C minor chord and an Eb major chord. C minor and Eb major are relative keys; they both have all of the same notes, just starting in different places. Since "You Don't Believe" fades out at the end, there's no resolution, so it's sort of ambiguous whether the song is in C minor or Eb major (if I had to guess, I'd say C minor because it starts with a C note). Tonally, it's like the song is alternately pulled toward either C minor or Eb major, and that same sort of division is in the lyrics. Each line in the verses contains both "my" and "your."
First verse:
My eyes with your visionSecond verse:
My choice but always your decision
My play with your direction
Well it's my lead but always your connection
My words, your expressionThird verse:
My land, always your possession
My song, your production
My expense is always your deduction
My fame, your reflectionIn each line, possession is alternately first person ("my") or second person ("your") in the same way the song seems to be alternately in C minor or Eb major.
My weakness always your protection
Well it's my terms on your conditions
And they're my tunes but they're your compositions