Finally got some photos, to further explain what is going on.

I ordered type A camera, the thin one.


However, there is no plug and play way to install this on the E53. The E53 license plate is different from say E60 license plate, where the bulb is held in a separate case and you can detach the whole case and replace the case with the camera.

On E53, the bulb sits on a small thin board and the bulb is case is a common body with the whole plastic trim. The only way I see this through is wrecking the board. The problem is that I can't get a clear view of the whole board and I would avoid wrecking it since it also holds my soft-close button.

As about the blur, by your description, is surely sounds like condensation. I've been fighting this when I got the camera from the car and took the photos above. I had to constantly wipe the lenses and quickly get a shot before it went blurry again.