Oh yes. The aux. lamps get power from the headlight low beam wire. That's why they go off when the high beam is switched on.Seems like the problem is farther upstream than the connector. A bad connector would not affect the aux lamps.
Check the connector for the left hand control switches, unplug it and make sure all the pins are in correct position and not pushed back into the connector, check the blue wire.
Check the key switch ignition relay.