Though some areas of the shop manual call this item a cable, the parts books refer to it as a wire. Specifically: Wire, direction signal actuator (found in group 2.913). Group 2.895 does deal with a lot of the other directional signal parts.
There was an early and a late part number for the wire and parts pkg. Use #1960533 for the early part, for cars with .065'' wall thickness on the steering column jacket. The late part is a #1962876 for .095'' wall thickness jackets (also used on 64 models). Part #1962877 is just the parts package, the tube and clamp.
Dealer letter 63-6 details how to adjust the switch on tilt wheel cars. On some early production cars, the switch may need new mounting holes drilled in the mast jacket for correct positioning. Let me know if you need a copy of this letter or the parts lists.