My 30amp relay must have been too big then. I tried using some 12V/30AMP relay (some poor brand) and the screen kept flickering. The relay kept on opening and closing (that buzzing sound), and the camera was going on and off. I will try a 15 amp one.

The weird thing is that I measured the reverse light power and it came up as 10V instead of 12V. As far as I understood, the LCM actually sends pulses (only visible to an oscilloscope, hence the filament of the reverse bulb looks like it's continuously on) to the reverse light instead of constant power. I will probably drop the reverse light wiring and aim for the PDC pinouts as soon as I figure their order inside the bracket.

I used exactly the following scenario:
Camera +12V = Reverse light +12V
Camera ground = Reverse ground
One Relay as follows:
85 = Reverse light +12V
86 = Reverse ground
87 = Reverse ground
30 = Pin 17 of white connector on TV module
(I had the 87a available but it is useless in this application)

The screen kept flickering, which may be one of the following reasons:
-I've got 10V from reverse light on Pin 85 of the relay, probably not enough to switch it -or
-I've got 10V from reverse light on Camera +12V, probably no enough to keep it alive