Those brown stains might be just surface rust. Take it apart and clean with diluted Simple Green or equivalent and a brass or stiff bristle brush. Dry thoroughly with a heat gun or hot sun.
Coat with boiled linseed oil to retard rust. After a while the BLO will harden and preserve your original paint.
That’s how I do it.
Here is how a Reed 1C of mine came out after that treatment.
Before and after