575M -fitting reversing camera -wire routing through bumper?

I have purchased a small reversing camera that I will fit, with double sided tape, between the two number plates lights. My plan is to drill a hole through one of the number plate lights to route the cable into the car. This light fitting would be relatively cheap to replace in future if a future owner wanted to remove the camera.

I want to parallel-route the number plate wiring with the camera wiring until it is inside the car, and then I'll route the camera wiring forwards, which is relatively easy. My problem is that I cannot see how to feed the camera wire through what is (I believe) a fully contained box section within the rear bumper. Please see the issue described with photos below:

The wiring loom for the numberplate lights go through a hole into the rear bumper section -see photo below

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I have tried to feed pieces of wire, cable ties etc through each hole, but they only go in a few centimetres and then get held up.

Has anyone done this themselves, and if so, please can you say how you have achieved it? I do not want to drill any new holes in the car, and I want any installation to be completely removable in the future. Any help is much appreciated. Thanks.

 

Many thanks DSD, I would appreciate that. I can see no other way to route it, but the issue is how to feed the wire through. Taking the bumper off might help, but I'm not in a position to do that in my garage. Thanks.