Some electrical gremlin must be having fun with the new head unit I'm trying to install

The problem is my new reverse camera not powering up and I traced the problem to the 12V wire that is supposed to supply the power.
Both the camera and the RCA signal cable are fine - I know because I tested them with a separate power adaptor (i.e. from the wall socket) and the head unit displays the image from the camera just fine.
I tested the 12V power cable however and it was only giving me 9 to 10 volts and strangely fluctuates a fair bit.
That 12V power cable is connected to the head unit's ACC cable with a T-tap connector. I had another equally long cable T-tapped to the same ACC wire and that is giving me a steady 12V.
Any obvious ideas I should check for before I pull the head unit and all of the trim panels apart again? I'll probably break a few more pieces of plastic doing that...

My chief suspect right now seems to be that T-tap perhaps not done right.