Hard to say without further inspection, but I suspect it is "surface rust" and not rust through from the inside of the tubing. If it is rust thorough, you have a much bigger problem.
More than likely a crack developed in the paint around the cable guide brazing, allowing water and air to penetrate under the paint and oxidize. The oxidation has spread under the paint. You're on the right track - have to get down to bare metal and remove the oxidation, then seal it/repaint. What are your painting skills, what paint equipment do you have access to, and how seamless do you want the repair to be?
A Dremel tool would be a big help in preparing the surface, but you can do it by hand with a lot more elbow grease. Some stripper, wire brush (or brush tool for Dremel), varying grit sand paper or grit wheels, steel wool, masking tape, and maybe some muriatic acid. Spray cans of metal primer and some white acrylic enamel and clear coat will patch up the spot after you get the oxidation cleaned up; however, unless you have really good paint skills (and especially with a spray can) the repair will probably be visible. Unless you get ALL of the oxidation and completely seal the area, it will return again in the future.
The alternative is a professional painter and/or a local shop that has a bead blaster to prep the surface. Depends on the value of the frame and how much you want to spend.