Dipped lights to come on with full beam

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You can't flash the HID bulb, so yes. The bulb is tucked under the projector and not really visible, anyway.

The relay, as wired above, will make it so that when you pull back on the stalk with the headlights off, the halogen bulb is used. When the headlights are on, the HID high beam solenoid is used.
They are never on at the same time and the halogen bulb is used for daytime flashing only.