speedometer/cable noise - help requested

So when rebuilding my latest Dart (1970 Dart GT - standard long speedometer - not rallye) I took 3 speedos to a local guy that works on dash components. He ran them on a bench machine, picked the best one, lubed it and I installed it with a new cable. All worked fine for about 8000 miles. Speedo worked fine, jived with the speeds on my GPS, no noise. Then it started. It took a while to figure out that the noise that I was hearing was from the cable or speedo. The sound is a vibration and a cyclic squeal like a small bearing going bad, and it's getting worse and worse. finally I noticed a vibration in the speedo needle that matches the sound. I took the cable loose from the trans and voila... no noise! It seems to be coming from the cable as opposed to the speedo itself? In 50 years of working on and driving 70 Darts, I have never encountered this! So how does one lube the cable? Will it just pull out of the casing? What should I lube the cable with so that it is silent? Can I pull it out from the trans end, reinsert it and then twist the cable from the trans end until it engages at the speedo?

Thanks in advance for the help!