I'm not sure about the 2010 but I would assume it is the same as my 2011. Right above the drivers side kick panel and towards the door opening you will see a connector that has a white, blue and an uninsulated wire (shield). You can tap into the white and blue wires and run it to your nav unit. You will have an image in both the mirror and the nav unit or you can disconnect the connector and tap the wires that are routed behind the kick panel and run to your nav unit and you will have video in the nav unit only.
I realize this is a Sierra forum, but it was the first one I found talking about what I was looking for. Has anybody tried this? I have a 2011 Yukon XL and it came with the backup camera and display in the mirror. The navigation is being added in a week. I dont want to switch it, but if I could have it in both, I wouldnt mind. The mirror makes more since to use, but the nav is a bigger screen. I assume it is not just an RCA cable connection. That would be too easy.