Well, I think I have things solved. One solution was very simple, and two were very weird.
For the reverse lights, taking apart the connector at the kick panel, spraying some dielectric and re-installing did the trick.
For the brake lights, the connector on the switch had rotated around the switch housing so that the plunger couldn't depress. Realigned the plunger, and the left brake light started to work.
That last remaining tail light was really weird. I finally got to the point of dusassembling and studying the socket. Sure enough, there's a little tab on the plastic piece that's supposed to locate the terminals properly, but it was about 90 degrees out. I guess I must have man-handled it when I put it in. Realigned that little plastic piece (shown below), and the right tail light and brake are functional.