I realize these are bad pictures. It is difficult to take good pictures of black on black. On the left is the outside of the back with the piece sewn in. The match is better than it looks in the picture. I was trying to create contrast. The inside is to the right. I tucked under the edge of the lining and tacked it to the seam. It looks like there is just another set of seams in the back. The problem areas are the center back vent and the collar. In place of a single vent, I made the added panel into a flap that looks like two vents fairly close together.
I also added length to the sleeves and made them cuff to cover the seam above the wrist.
Next I will make him a vest. He needs it because adding only to the back of the jacket means it doesn't close in the front. I don't have a pattern for a man's vest. But I don't really need one since this fellow is very tall and very slim and any pattern would have to be modified beyond recognition anyway.
Based on my measurements, he's actually a true rectangle. A very long rectangle. So I made a quick muslin (pinned only) and have since cut out the fabric. I decided I could teach myself how to make a welt pocket on this project.