During my long ride last night (with the slipping chain), I was very attentive to the bike, and eventually I figured out that when I applied either the front or rear brake (causing current to flow to the brake lights), the headlight and speedometer backlight dimmed slightly.
(This took a long time to figure out, because squeezing a lever and pressing a pedal feel like very different actions, and I didn't correlate them until I applied an overlay of "engineer's mind.")
What does this mean -- that my battery isn't putting out enough voltage? And what in turn does that mean -- that my battery terminals are dirty?