It is definitely a ground problem, either at one of the lights (or sockets) or the dash ground under the instrument panel.
Check all the bulbs first to make sure a corroded socket is not causing the problem. Then verify that every light assembly is grounded using a star washer that cuts into the metal. There are probably two grounds on the rear (one each side), and four on the front (headlights, and each park/turn socket). There might be separate grounds for the side marker lights.