I know I'm bumping an old thread but hopefully the information I provide will be of use to anyone in the future who attempts this.
Following the previous posts and personally going out and ripping apart my dash I can conclude with absolute certainty that the 2012 Si WITH Navigation is NOT back-up camera ready. I took apart the navigation unit and concluded the same as previous posters have that the hardware simply is not there to enable an external input onto the screen. I know someone mentioned you could highjack the navigation display but that would require an extensive amount of work and given that these cars are older now, there are more economic options available.
So can I add a backup camera to the 2012 Si with Navigation?
A: The short answer is yes, but it requires you to swap the IMID display from a 2012-13 car without navigation; the IMID displays found on cars with navigation is a completely different unit than the one found on Civics WITHOUT navigation.
The part numbers are different in Canada and the USA but the fact that they are different parts is still true.
The most economic option I have found was to simply swap in a used IMID unit from a 2012-13 Civic WITHOUT navigation. This part is imperative, you MUST get a unit from a car that did not come factory with navigation. They are completely different parts with different part numbers. I have verified that the 2014 IMID unit does not work either, even if it's from a car without navigation. It absolutely must be from a 2012-13 Civic without navigation, no exceptions.
I have also confirmed that you can swap an IMID unit from an LX/EX/EX-L to the Si, although you will lose the instant fuel mileage and power usage display. You will also be met with an "eco off" display whenever you turn the car on. I imagine swapping from an Si to an LX/EX/EX-L would also work, but I have not verified. The connections are all the same however.
