I wonder if it wouldn't be more helpful, and less dodgy with the authorities, to tap into the other reverse light with a mounted white LED? When I lived in the UK, I had to retrofit my vehicle with an mounted fog light - you could follow this same principle and get a low profile LED.
It's not too much work to convert the fog into a reverse light, however I find my lighting still insufficient.
Only require a piggy back clip and wire really. Pull bumper off and cut the fog lead, joining to a wire that you will run across the back of the bumper to the other side. Piggy back onto positive and seal them up! To replace the bulb you may have to shave off one of the prongs as an offset 12v 21w isn't easily found in clear/white.
While I had the bumper off I piggybacked some extra wires and cable tied down near the exhaust in case I decided to put in another reverse light, which I will now. Won't have to take bumper off a second time so will be easier!