Is it possible to install an OEM backup camera to Toyota Corolla 2016 L

I hope i'm posting this in the right place.

I have been trying to install an OEM backup camera to the base Toyota Corolla L 2016 model. I found a kit on amazon that plugs in to the touch screen (still can't post links) but I prefer the OEM camera.

The rear trunk trim molding of my Corolla L does not have the cut out for the camera.

I found one on ebay with the cut out.

So I guess I can easily replace it. I also found an OEM backup camera

and here's how the connector looks like

The problem is the wire that connects from the OEM camera to the factory touch screen. Any idea where can I find it? or At least how to convert the connector in the OEM camera to a normal aftermarket camera connector so it could work with harness on amazon?

I'm hoping to get the OEM look with the OEM parking grid lines.
yes I checked but I couldn't find the camera connection in the trunk. I'm pretty sure it does support it. I have seen people installing the aftermarket camera to the entune factory display (the same model L), and there is a kit on amazon that contains the wiring to plug right into it . [search for item number B00MSIQFRO on amazon] (can't post links yet)

However, I did not find any information on the OEM camera. As you can see the camera has 4 wires (BLACK, RED, WHITE, GREY). If I can find a way to convert it to an RCA video cable or to the aftermarket connector that would be great (I'm not sure if the grid lines would show up in this case).

here's a picture of the wiring harness the plugs in to the factory touch screen to attach an aftermarket camera (from ebay).

this is a picture for the back of the radio/display from amazon (Not my pic. I did not disassemble the display yet)

It would be much better to find the OEM connector but I couldn't find it anywhere. I don't even know the part number.
Any luck on this? I am trying to do the same thing, any recomendations? Does the basic L radio support the camera and does our L model have the camera harness or do I need to purchase one?