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I don't remember if the headlamps will shut off when starting the car or not. The brake causing the headlamps to dim however, you probably need to pay attention to the battery cable connections to both the battery and the starter solenoid.
My headlights have been dimming when I put on the brakes since my '01 was new. All my connections are tight and the battery is strong. I think its just a poor electrical design feature, sure is annoying however!