I've worked on lots of POS BSO's and my method of attack is to spray it down with Kroil, work back & forth, sometimes need a screwdriver/lever/wrench to get it moving. Keep working it and spraying it. Once it's halfway freed up you can use the cable to move it. When it's moving well enough for the shifter to work acceptably I'll clean it off and Tri flow it.
Really bad I might hit it with a torch to help loosen things up too.
https://www.amazon.com/Kano-Kroil-Pe.../dp/B000F09CF4