OK, here's my suggestion:
Use a #12 or larger wire for ALL conductors. The headlights pull a considerable amount of amperage, and the smallest wire in the circuit is the choke point. It would be like supplying a fire truck with a garden hose, and expecting it to pump lots of water, if even one wire is smaller gauge. A 6-volt system needs heavier wire than a 12-volt.
The headlight relay is supposed to mount close to the lights, and shorten the path for the heavy current draw. The dash-mounted light switch just turns the relay on and off in that case, so the wires to the switch can be smaller without a problem. Make the wires to the relay from the battery, and from the relay to the lights heavy enough to carry plenty of current. ALL ground connections should be clean and tight, and should be attached to a a well-established ground, like a frame rail or engine/transmission part, not sheet metal.
Good luck!
Jerry
