Starting fresh this morning, and with better light, I was able to solve the riddle of the connector. If anybody else needs to know, there is a U shaped slide around the plug, with the closed end at the front of the car. Two pegs on each side of the plug (at its base) fit into diagonal slots on the slide. Using a screwdriver at the closed end of the U, you can GENTLY work it toward the front of the car, which raises the plug up out of the socket as the pegs slide up in the diagonal slots. I believe the pull-out clip at the rear of the base serves as a lock.

Furthermore, there are indeed two bundles of wire coming out of this plug, and only one comes with the new harness. The second bundle is from another harness and goes to a separate plug which you must move from the old plug into the new one. This is easy, since it just slides out the open end of the old plug and you can see how it fits into the empty slot in the new plug.