Cable testing
I did a careful job fixing the cable and checking the continuity and resistance of each line. I even opened the basestation to measure conductivity all the way through to the PCB, to make sure there was not a problem with pin length or mating.
Unfortunately I was still getting the amber light.
This is where I started to get nervous, because @thetechnobear said John has warned people that opening a 'harp could require the keys to be recalibrated. But after enduring a few months with no other prospect than fixing it myself, I decided to open my Tau.