I have only dealt with light spot / surface rust when cleaning cast iron cookware.
Cleaned it up by scrubbing under warm water, or with household vinegar (5%), or citric acid, and some light scrubbing.
In the Cast Iron Cookware thread on AS there were some comments that soaking CI in vinegar for long periods can damage it.
I have used electrolysis to clean up rusty tools, and had good experiences with that.
Some people use it to strip cast iron pans too. I use a lye bath, and try to do it in batches. But electrolysis might be better for 1 or 2 at a time.
Just remember that removing rust does not replace lost metal. This can be a issue with cookware, if on the food contact side, or just cosmetic on the outside.
Philbert