After reading the suggestions about thread & a magnet. I decided to try thread & vacuum. I taped off all the openings except the inlet & outlet. This worked OK to suck the thread through, but I had problems migrating from the thread to the cable. After investing 30 minutes with no success, I tried a different approach.
I was finally successful in just a few minutes with a several foot long section of 1/16" welding wire Taping the cable to the welding wire was no problem & I had no "premature release" difficulties. I did put a moderate bend in the wire, though, to enable me to steer it to the outlet hole.
I have a somewhat recent Silvio frame (#54), that has the seatback center cut out so fishing the cable through that area is no problem.