Yes, you can do this with a Tazer JL Mini programmer. After feature is programmed, the rear camera will stay on as long as you want... With the programmer you can also have a front camera.
With the Tazer....
The double tap of the mute button turns on the camera and it will stay on until you press the X on the radio screen, or double tap again, to turn it off. So, another words, the camera will stay on until you turn it off.. no 10-15 seconds and then it automatically, turns off.
I have a 2018 Sport , 2 Dr. On the side of my base display is a "more" button, and a rear camera choice. So I can turn my rear camera on any time, and it stays on.
Pretty good for a no frills Sport !