Under normal daytime driving the display on the radio will go blank when you step on the brake pedal. If you turn on the parking/headlights it's normal. There seems to be a separate circuit for daytime driving vs nightime. When headlights are on the brake pedal has no effect on the radio display.

 

Probably a bad ground.

Remove the kick panel on the passenger side and inspect the grounding studs and their connections looking for loose or corroded connections. Repeat, if necessary, on the driver's side.