Dose this have Day Time Running Lights?
The only thing in the circuit that I can find, that would match your description of the problem, is the control circuit to the headlamp relay from the head lamp switch. The combination switch has two parts
1-headlamp control, 2-dimmer function. When you flash you H-beams the HL-relay is energized momentarily. When you turn the headlamps on it's energized until you turn them off.
Confirm the HD-relay is commanded on during both selections. There is a splice in the harness making the connection for the two functions to energize the relay independently.
Good luck, Cheers