Flap on, flap off folks. I've found it.
The pipe was indeed broken. It had broken inside the rubber pipe that's connects to the tailgate to the body. Happily, it had broken at the connector. As a test I cut of the piece of broken pip and connected everything together. Full function was restored!
I will be effecting a proper repair. I have a piece of fresh pipe that'll sit inside that rubber thingy (The old pipe had gotten hard). Then I'll use another connector to splice the other end of the new pipe.