I routed the wire how the factory drawing showed it. I wrapped it around the back side of the hinge and installed the clip on the left side. By looking at the bends that were present in the wire, it looks like it is installed correctly now.
The only issue I have now is that with everything hooked up, there isn't enought slack in the dome light harness to clip it in the topmost strap on the wheelwell. Maybe I have the dome light harness in wrong.