ya - after reading more from the links above, that's what I figured. I think it's going to be pretty tough to find an existing cable at a modern bike shop.
I don't quite get how things connect inside the twist shifter, so I'm not sure if there were two inner cables that attach at each end, or if there is one long inner cable that goes through the twist shifter and locks in place there somehow. As mentioned above, some restore specialists may be able to help.

If the rider does not mind "single speed" you could maybe put two small, but long bolts (machine screws, maybe #8 ) through the holes where the barrel adjusters go, and with a nut on each side, adjust the bolts till each touches the shifter lever and holds it in a single position. You could then adjust it to the gear the rider wants to use, and lock it in on that cog.

Something like this sketch. (not to scale)