I had to replace the wire on my truck and as I recall, once you have opened the switch case, the bakelite block just pushes out from the back. The armored cable is just pressed into the back of the switch body and you have to remove that first. Then you can push the bakelite block out from the back where the wire exits. Perhaps a little WD40 will help loosen things up.

Kent

1937 Chevy 1/2 ton
1942 Chevy 1/2 ton
1947 Diamond T Model 509
1951 Chevy 1/2 ton
1950 Chevy COE Model 5700 ~ "Barney" ~ And more pix