Update:
I bought a new switch from American Classic Parts, the Stovebolt sponsor, and I'm happy to report that the switch they offer is Made In USA! If that doesn't lure you to buy from them, their price will.
I replaced the old one using 3B's instructions, and now all lights work as designed.
I probably spent 10x as much time chasing down the problem than it took to simply replace the switch.
If anyone needs to do some night reading, stop by my truck. The dome light works wonderfully. Thanks to Bill and 3B for the help.
Bill