Thanks for your advice, batman. However, I'm sure the problem is the cable.
I checked the front switch and determined that it was not the problem. I checked the rear switch and determined that it worked properly. I checked the cable and determined that nothing moved along the parts of it that I could reach when I depressed the brake, no matter how hard I depressed it. I sprayed penetrating oil onto everything I could reach and tried again the next day. No movement at all. I concluded that the cable was frozen in the "on" position, which is why the spring isn't moving and the switch is always on.
I'd rather replace a 12-year-old, corroded cable than try to un-stick it, so I'll do that when I have a replacement cable, which I've ordered. I also try to disassemble only what I need to, as I've broken bolts on this bike before, despite repeated applications of penetrating oil, heat, and cold.
Thank you all for your help. As I mentioned, I'm somewhat spatially challenged, in terms of visualizing, and the photos, videos, and explanations really helped me understand how this was supposed to work, and then to determine what wasn't working right.
David
batman wrote on 05/31/19 at 12:25:08:Why do you think the line between the pedal and the switch contains a spring at all? It's there to allow you to "cover" the brake pedal ( place your foot on it, and slightly depress it , to prepare to stop or slow if need be ,without actually activating the tail lamp's stop filament .You have two ways to deal with it ,you can lower the switch , allowing it to retract the 1/4 inch it needs to go off , or loosen the nut on the end of brake cable to allow the pedal to rise slightly making the cable have slightly less tension again allowing the switch to retract and the light to go off . Perhaps it's time to go out to the bike and actually try something. If that fails perhaps ,because your bike sits out you may try greasing the back of the brake pedal and the cables as that is standard maintenance (every 12 months/4,000 miles .