I figured out the way to do it.
The second wire has to be attached to the middle copper colored piece. I bent the thin little tab up and used an exacto knife to trim a small amount of plastic away from under that part, so that it wouldn't melt when I soldered the wire to the tab.
For testing I clipped the new leads to the rear light and left it alone, after closing the doors for 10, 20, & 30 minutes. Didn't turn back on by itself.
Fully installed it works like it should now. Automatically on with the doors and fade off or manually on or just off, like the dome light!