You have a 30 year old bike, you have oxidization, for sure.
A dremal is overkill, sandpaper is fine, fine sand paper is better.
There is more then one ground, any place that is connect to the frame.
Usually you can visibly see if a bulb is broken by a break in the filament. You could also hook the bulb up to a 9volt.
If the head went the tail light probably did too, depends on how the bike is wired.