Our vintage cloth push-back wire is 22AWG stranded wire, with textile braid made by Gavitt. This is the same wire used by Fender.
Ours has a tinned overcoat after the individual strands of the conductor are twisted together locking the strands into a single unit just like Fender has their wire made.
The benefit to this process is that the wire holds its shape very well without having fraying strands at the cuts needing to be twisted and tinned, making it very easy to work with.
The cloth push-back insulation reduces work time by eliminating the need for wire strippers. Just cut to length, push back the cover and solder into place.