When I was tightening the screws in the clutch, I accidentally pinched this cable (quite harshly), and I think I might have destroyed it. What is the function of this cable, and should I attempt to fix it? The clutch seems to be working though.
I don't have the Inverted pedals. I have the standard V3's. But my guess would be an rf ground cable. All that metal acts as a nice antenna for rf interference.
Replace it with same gauge wire, and ring terminal, and you'll be fine. If there is enough length of original wire, just cut and splice with a Western Union wrap and solder. Then heat shrink it.
It will work until it breaks, and then will probably work until you experience rf noise issues in your hall effect transistor. Which may never happen, but if it does, it usually manifests itself as "flaky" response/function of the clutch.