There's a menu in settings that shows you the test signals. First verify that you are getting the high and low signals correct as you shift in and out of reverse.

 

Also, if you are doing 12v with reverse, make sure you don't have to option set to to Ground in the Camera Polarity setting. Sounds like you might have it the wrong way round.

First of all your installation is wrong for the camera. Connect the red power wire from the camera to the red power wire of the unit and you will get rear view. Next what color is the camera icon on the screen? If it's blue touch it again till it's white and your other problem will be solved as well.

Fruitbat04's suggestion put me on the right track.  With no change in the "Connection Status" in the Settings Menu when shifting to reverse, I figured the problem was in the reverse wire connection.  Today, when I backtracked the wiring from the head unit to the truck's wiring, I found that although the Metra harness has a reverse wire to connect to the head, there's no matching wire from the Metra box to the truck wiring. I called Metra to confirm it, and got an "Oops" from the support tech.  That harness looks for the reverse signal in the ECU data link, and my truck's ECU doesn't provide one.  It needs it hard-wired.  I told them an asterisk in their instructions would have allowed me to get correct connection the first time and saved me hours of troubleshooting. I simply ran a direct lead from the AR3's violet/wht wire to the back-up light circuit and, voila, automatic back-up cam and rear view mode work as described.  It had absolutely nothing to do with the camera or power.

So your cameras power wire is still connected to the reverse lights? How is the camera getting power for rear view if the reverse lights aren't on?

It doesn't really require it. Lots of people run it like that if the 12v from reverse lights if it's more convenient than a permanent source, as when do you ever need a rear view camera when you aren't in reverse?

So your cameras power wire is still connected to the reverse lights? How is the camera getting power for rear view if the reverse lights aren't on?

I explained earlier that I initially connected the cam pwr to the back-up lights because it was convenient and I don't have much use for the RVM since I don't tow anything. When the screen wouldn't automatically switch to the camera view in reverse, I moved the cam's power to a full-time powered circuit. Since the problem continued, I kept digging and eventually found the deficiency in Metra's $90 harness.