They might be wired in series, but I don't know for sure.
If the problem with corroding bulb sockets keeps happening, scape them clean like you did before, then get some "electrical contact cleaner" and liberally hose each terminal with the stuff. Install NEW bulbs and be sure to put a dab of silicone or di-electric grease inside the socket. It will help prevent mousture from getting in there and help keep the plug from corroding again.
