Checking out YouTube on the subject will show several videos on the use of a UK product called Harpic, a caustic toilet bowl cleaner. The edited videos make it look effortless, so I grabbed our Walmart bowl cleaner along with some Lime-A-Way and Rustoleum gel rust remover. I also gathered four grades of scuff pads and set to work at a home-brewed comparison.
As it turns out, Harpic is 10% hydrochloric acid and mine uses sodium hypochlorite which is likely lacking the same etching power. In any event, as I progressed through the various products, I was slowly getting results but doing a lot of scrubbing. So I decided to try some light grade sandpaper — 1200-grit wet/dry. Things went much quicker but I eventually realized that sandpaper and water alone achieved the same results just as quickly as any of my products. In particular, the rust remover didn't seem to do a thing, which tells me that the discoloration isn't a rust issue.
(click on an image to enlarge)