This video was helpful because it showed me how the cable is held (the metal cap for both the flange and the cable itself). But it doesn’t tell you about the little retaining wedge at the end of the plastic pin. For future users: there is a small plastic wedge that needs to be pressed to remove the end of the cable ring. Here’s a screenshot from the video, with the wedge sketched out:
I used a screwdriver jammed between the base of the pin (actually, the door lever) and the ring, to give it some weight. I used a pair of needle nose pliers to press the wedge in. The preload on the screwdriver allowed him to only started to slide over the wedge, but I still had to do some prying to get it completely off the pin. It’s a PITA because there’s very little room to work with.
