I've installed a few backup cameras, so let me see if I can help you. I am not however familiar with the pioneer headunit, so that may issues. Lets first start with a better understanding of your symptoms versus goals.
Are you trying to have it so that you have the display show your backup camera source when you go into reverse gear?
Typically, the way that works is by having the camera power or camera power trigger line wired into your reverse light, so that your camera is only on when in reverse, and your not drawing current all the time on it. Some actually put a threeway switch in there for reverse or manual activation.
I'm not quite sure what you mean by purple double din, if your trying to figure out which the reverse wire is, I would pull the back lens and check the color or the wires on your reverse bulb. It is two screws to swing it out. I can't remember exactly which color it is, etc.
You also mention that when you select manual, I presume on the pioneer unit, you can get the image. Are you talking the camera image?
If your camera is already working, then its up to understanding how to set up the pioneer unit so that either is always on the source channel for your camera or if it switches to that active channel, some don't. Typically there is a default channel or way to set up through the unit to switch to an active source. Then it is just a matter of wiring your camera trigger, or power depending on the camera, to your rear lights.
If you can answer those two questions and maybe describe to me the way you have it wired, and more importantly, what wires you have and what they do, that would really help. Also just what your intent is as far as overall goal. There are just a few too many configurations to know how best to answer help given what you've said. But there are only a few ways to do it.