I, occasionally, have the same problem on my '03. What I've done is to remove the bulb and clean the wire shaped contacts with a pencil eraser. I ground the eraser into a "V" shape on two sides of the eraser. That way, you can get it into grooves in the socket where the bulb lives. The eraser is slightly abrasive and seems to take the offending corrosion off the metal contacts. Then, I put some dielectric grease on the contact points and that seems to solve the problem, for awhile. I live in the desert of Phoenix, AZ. so I don't get as much moisture as you do. I have no rust like you do. If you can get that metal cleaned-up, maybe spraying a silicone product would keep the moisture off. I don't know how long the silicone would stay on. There may be a better product to rust-proof that metal.
Joe F.