I recently had this issue (rust spot near the "o" on the case back) with a 50yr old Mido Ocean Star I purchased. I would like to share my experience and the product that worked with this community. I first tried vinegar and Hammerite Rust Remover to remove the rust, but despite several applications, neither removed any of the rust (see first picture). I figured I would need to polish it off, but I am not a fan of polishing and risking removal of too much metal. I decided to try a product I use to remove scratches on acrylic watch crystals called Quixx Acryl (second picture). It is marketed for cleaning acrylic components on automobiles, but I have used it to clean and remove scratches from acrylic watch crystals for awhile and it works amazingly. My thinking was that the abrasives in the paste are very fine as it is intended for plastics, but may still be strong enough to lightly polish metal.
I first applied a small dab of the paste, then rubbed in circular motion for 1-2 minutes, followed by a rinse with water. After one application, 80% of the rust was gone. I repeated one more time, and the rust spot was completely gone! Further, the product was also able to remove most of the scratches on the case back metal. I am used to masking metal when I am doing acrylic, but this stuff is also a great and gentle metal polish. FANTASTIC all-around product for watches. I would not choose it for deep scratches, as this would take a lot of work, but for smaller abrasions and light rust it is awesome!