There are total three wires in the OEM camera connector, as per the picture you have attached. Their function, though need to be confirmed, can be described as follows
1. Red - 12V (available only when reverse gear is engaged)
2 .Yellow - video output signal from the camera
3. Black - ground (video + power)
So ignoring black wire won't show any video infact this won't turn on the camera at all.
Try to make use of heat-shrink tubes instead of normal insulation tape on wire spliced joints.