Okay then.... sounds like you are already planning to do as some suggested and paint the entire tubes in the rear, but not the entire frame.

My.... IMO... don't strip to bare steel unless the paint is so far gone an has rust blooming through it everywhere. Just sand the bad places that already have exposed steel and use a high build automotive sanding primer. You can get that in a rattle spray can. Plan on multiple coats and sand between coats till it's even with the original paint then prime the entire tube and paint.

As much as I despise rattle cans for a final finish, the small amount you are painting makes them the most economical and convenient. Take a look at all the touch up colors at the auto supply stores. If you can find the local automotive paint supply stores....even better. You can use the Krylon and Rustoleum paints at the big box stores. They'll work well enough. The newer rattle cans tend to have less information about what they actually are though, so be careful on mixing brands and make sure to follow instructions on additional coats. Wait too long or too little between coats and you get some ugly wrinkles with some of the Krylon/Rustoleum I've used recently. I think that would be less likely with the rattle cans that are specifically for auto touch up.