There is one more method that would quite accurately pinpoint the
location of the problem and it's using a device called a TDR (Time
Domain Reflectometer).
We use it at work all the time to pinpoint problems in RF transmission
lines. It can, quite reliably, tell you how far from the end of the
line to look for a short, open or what have you. Unfortunately it's
beyond the budget of an average backyard mechanic.

In any case, good luck. Keep me posted what you find. I'll be more
than interested to learn where the problem was.