Seahunter

The back up camera on my 2011 has been balky for a while and now it never works.
When I put the truck into reverse, I get a blue window where the picture ought to be in the rear view mirror. The blue window lasts for about 5 seconds and then - nothing!
I'm 6 months past warranty and my service guy says it's too expensive to repair - learn to back up the old fashioned way.
I can back up just fine thank you but I want the camera. It's great for hitching up and anyway, it ought to work!
How do I determine what the problem is?
How do I know if it's the camera, the mirror or the wiring?
Any help would be wonderful.