I appreciate and think I understand your post. In your case, the original installer had connected the HU reverse gear signal wire (violet/white) to the positive lead of the camera. If I read your post correctly and that was the situation, your camera would not have worked for two reasons.
First, your camera was not getting any power. The violet/white reverse gear signal wire at the head unit is an input, not an output. In other words, the violet/white reverse gear signal wire at the HU only has power when it receives it from an external source, i.e. gear shift wire, reverse light. T