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I had the same problem. First check to see if they even light up at all. Turn on approach lighting and then unlock the car. All the lights should light up except the headlights. If they turn on, then you know the bulbs are good. If they don't turn on, then start by checking fuses, or replacing the bulbs.
My lights worked when I unlocked the car, but not when I was actually in reverse. It ended up just being a backup lamp switch. $12 from Napa
Mine did that except about one time in ten the lights would still work. Turned out to be the fuse even though the element wasn't burned out. One of the blades was wiggly having broken off down inside the plastic.
Where's the switch located on an A4? My reverse lights work when the keyfob is pressed, but not when shifting the tranny into reverse. Any suggestions? The relay checked out fine.