I've used modern teflon lined compressionless housing meant for index shifters with Sturmey 3-speed stuff in the past and it's perfect. I would guess brake cable would still work fine as well, the tolerances are quite loose with Sturmey 3 speed stuff.
Yes, seconded with benbrangwyn. Check the hub itself is ok and pull on the rod to make sure the hub is ok, flip the pedals round back and forth if you have the bike on the ground as it won't shift under load. It's rare that the older 3 speed hubs go bad internally, usually they are out of adjustment or gunked up inside. Give it a few drops of motor oil or ATF fluid (avoid 3-in-one or sewing machine oil as they are too thick) in the oil port. Watch out for any excess fluid spilling out behind the sprocket running all over the braking surface.
I've used modern teflon lined compressionless housing meant for index shifters with Sturmey 3-speed stuff in the past and it's perfect. I would guess brake cable would still work fine as well, the tolerances are quite loose with Sturmey 3 speed stuff.
Yes, seconded with benbrangwyn. Check the hub itself is ok and pull on the rod to make sure the hub is ok, flip the pedals round back and forth if you have the bike on the ground as it won't shift under load. It's rare that the older 3 speed hubs go bad internally, usually they are out of adjustment or gunked up inside. Give it a few drops of motor oil or ATF fluid (avoid 3-in-one or sewing machine oil as they are too thick) in the oil port. Watch out for any excess fluid spilling out behind the sprocket running all over the braking surface.