you've got a short circuit in one of those lights, or the wiring to them

Was the car ever wrecked? Did you move any of the wiring at any time in the past? 

I have seen wires that were routed wrong around edges of steel rub through and short out. I have seen body panels bolted on or back in place and pinched a wire or someone added a screw that went through or pointed at wires that rubbed and shorted. Look for BS. 

Also take the bulbs out of their sockets and look for broken pins, cracked insulators and debris in the sockets. If you carefully inspect these lights you will find it. 

Also look under the drivers side rug. Many harnesses are run under the rug and after years of driving these harnesses are crushed or worn through and short. Might have been cut or patched in an old wreck. Get in there and look for trouble. Its in there somewhere. Keep an open mind. Something is not going to be original, or tampered with, or worn out. Look for pinch points and places where sharp metal can pierce the wires as they pass from one part of the car to another. 

Those wires should come down the pillar to the left of your left foot, and under the rug or the trim strip at the door and back to the rear seat and up over the wheel well into the trunk. Examine them. 

Look out front on the daytime running lights and its associated circuits out in the front. Its common on old cars to have been in an accident or two with other cars or deer and just because they look good does not mean there is not BS hiding in the shadows as you look at the wires out there between the rad support and the lights/outer body panels.