Prius 2005 backup Camera

Hi everyone,
This is my first post, hopefully will be a great addition to the PRIUSCHAT family. as a bonus, I'll reveal the A-Z guide on how to do the installation professionally once done. this will save hundreds of dollars for anyone who's interested to have the factory head unit with a backup camera. this is only for Prius 2004-2005 with JBL and Navigation systems.
so, my question is kind of old, one: because it's about a 24-years question, and two: because it look like an old subject (but it's not, I think).
so, I have a Prius 2005 with JBL and navigation system. I have bought a cheap module that converts any camera output to RGBS which is compatible to the MFD I have and it works flawlessly.

The issue that I'm having is to identify which wires/pinouts are responsible to switch the display to navigation screen when reversing, and when done reversing, return the screen to the previous screen. In other words, the camera trigger.
Yes, I'm connecting the navigation screen wires to the converter I bought and disconnecting -permanently- the Navigation's ones, only the display wires, R, G,B and SYNC. All remaining wires are intact and the NAV ECU is connected and working properly. who needs it anyways?

Trust me, I searched online and I bought the wiring diagram book to find the trigger, but no luck.
I don't want to spend $250+Tax for the Module offered online only to add the backup camera capability.

Who can give me a way to switch the display to NAV screen when reverse, and when done reversing, switch back the display to the previous screen?
Reverse ---> Hit the Map Button on MFD
Reverse done ---> Hit the Map Button on MFD again to return back to the last screen

Thanks for helping