Hey, Mark & everyone! The code is gone! I (with your help) have done it!
When you wrote:
" I'd then gently place the switch back on the shaft and tighten it down ensuring that the switch stays in the aligned position".
that is what I was doing
wrong. Everytime I would tighten that center nut it would slip out of alignment.

But I thought that the van wouldn't start if even the smallest thing was wrong so, I thought everything was right.
Now I have to wait until my child wakes up to let me know if the
white lights come on when I go into reverse.
"A little trick of the trade, but you should always keep the old part until you have the new part in hand, installed and working. "
Good Idea! My new part came from AutoZone for $30 plus tax. I will remember that.
Thanks, Mark and to everyone who helped.
UPDATE: The reverse lights are on! Big Burgundy is fixed! (at least for now)