[nkaminar]

The grounding of the headlight bucket depends on good metallic contact of the bucket to the headlight bar and the bar to the fenders and the fenders to the frame. If there is rust or lots of paint that can restrict the ground. Use your ohm meter to test for a good ground and either correct it or run a ground wire to a place that has a good ground.

The connectors at headlight buckets, especially with repo parts, can be a source of problems. In my car the wires are lead into the buckets where bullet type connectors are used for the individual wires. The stainless connector is still used so that from the outside it looks the same as original.

It sounds like there is some error in the wiring or the switch. It will take some careful analysis to trace down the fault. Depending on what year your car is, you should have only parking lights when the switch is rotated left and low beam when rotated one notch to the right and high beam when rotated two notches to the right, but no parking lights when the headlights are lit.