I have a small TDR unit, but it i mainly for longer runs, I'll give it a go though. I also have a 4276A LCZ meter I can use though.
Using the 4276A, I get 3.3pF at the scope end, and the probe end is not really able to be read properly, the 4276A freaks out a bit but shows 0.02nF, and my 34461A goes out of range.
I remember reading that oscilloscope probe cables are deliberately resistive or something, maybe that could be causing the weird reading. If that is the case, I would assume that the break is near the scope end of the cable as there isn't enough of the cable there to throw readings off.
It would make sense too, if the cable was pulled while attached to the scope, that is where the strain would likely be concentrated.
Sound like a reasonable assumption?