I agree. Thanks for sharing it. I’ve been thrown for a loop many times and I always appreciate others taking the time to share their experiences.
It’s too bad that Popular Science dropped the Model Garage with its mechanic Gus Wilson. This series ran from sometime in the late 1920’s through 1970. Gus was always having to find the solution to a problem that no other mechanic could solve. OK4450, you get the Gus Wilson Model Garage award for this one.
I enjoyed reading these stories from the Model Garage from the time I was in junior high school. Although I am not a mechanic, these stories helped me in debugging computer programs and in teaching my students how to logically look for their errors.
Ditto TwinTurbo and JoeMario–Great puzzler.
I agree, it was something to stimulate the thought process. I don’t know what sort of VOM you have, but I’m guessing a nice digital. Those things have very high input impedance where a cheap analog meter has much lower impedance and might have loaded the circuit down enough to show the problem.
By the way, I once owned a 1980 Plymouth Horizon. Bought it brand new. One day, when it was just over a year old, it quit dead as I was driving down the road. I was close enough to home that I went and got my pickup truck and towed the car home. The problem turned out to be a wire that was corroded and broke apart inside the insulation between 2 connectors. Unlike your VW problem, at least this one was a solid failure. But, I shook my head at the very idea of a wire going bad in the middle of a run nowhere near a connector or pinch point or anything.
Glad y’all had a bit of fun with it although I think that problem took out the last remaining dark hair in my beard! 
I actually enjoy electrical glitches as frustrating as they are, and as bad as this problem was it pales in comparison to the VW one.
Hopefully no one will run into something quite this goofy but it’s something to file in the back of the mind if nothing else makes sense.