Quit. Removed, fiddled, reinstalled. Works!
First, let me say that BlueBobbyBird's photos were some of the best I've seen for troubleshooting. Thanks a million.
My 1999 F150 lost all but the high speed of the blower about three weeks ago. I suppose it could have lost the lowest speed, but I can't hear that most of the time anyway, so I really can't say it was lost.
Following BlueBobbyBird's photos and my Chilton manual, I was able to find the wire harness with its three plugs, and the resistor block.
I disconnected the three plugs of the wire harness and saw that the white plug of the wire harness had its plastic scorched and melted-away around the usual receptacle.
Then I pulled the resistor block and saw its corresponding conductor blade showed signs of overheating--the black plastic of the connector was melted around the blade corresponding to the receptacle of the white plastic plug of the harness. The three resistance coils were in perfect shape, and I think the thermal limiter was OK, too. (I measured it with a volt-ohm meter and it read high resistance one way and low the other, and I hope that means it's OK.)
I fiddled around, scraping the metal of both blades and receptacles--of the block and of the white plug of the harness. After about a day of dithering, I put the block back in and then reconnected the harness. I turned on the heater blower switch, and it again works on all speeds.
I'm guessing a high resistance developed at the contact between that particular receptacle of the white plastic plug and its corresponding blade contact of the resistor block connector. The high resistance caused heat and caused the melting. Eventually the resistance (from corrosion, probably) interrupted the current for all but the high speed setting. When I disconnected the block from the white plastic plug, this might have rubbed-off some of the corrosion products and left good metal. The scraping I did while the components were out may have helped, too.
Before I found that the speed control was working again, I ordered a replacement "blower resistor kit", Dorman 973-414, from RockAuto, and it is in the mail as I type, and cost $33.80, shipping to North Dakota. The kit has the resistance block and the white plastic plug with pigtail wires, so I'll just cut the old connector off and splice the new one into place and should be "good to go." I intend to follow ExTex's good advice and smear some anticorrosion grease on the contacts between the new block and the new white plastic plug.
As for the $33.80, I suppose I should consider that money an insurance premium, because who knows how long the "fix" I did on the old connector and the block is going to last?