Well, it looks like I'm in store for some electrical work near this branch of old wiring. After finishing Lost, I pulled the ladder out and headed into the attic to see if I could trace the wiring that controls the hall light upstairs. As I suspected, it was housed in that old conduit, which is a hallmark of older wiring. I certainly wasn't going to have any success attacking the problem from the attic, so I closed it back up and came down. (Aside: it's freaking hot in the attic.) My next step was to pull the light fixture off the ceiling and attack the problem from that side. That wasn't too difficult, and as soon as I had it hanging from the wires, I immediately spotted the problem -- one of the wires was broken. The black one -- the "hot" one. That explains the sparks I saw when I tried to change the light bulbs last week. So I enlisted yarbiedoll's help in turning the circuit off for the fixture -- she flipped the breakers and I tested the wire. We ended up partially mapping the breaker box while doing this and found the right breaker pretty quickly. Once I finished taking the light fixture the rest of the way down, my heart sunk a little when I realized that it wouldn't be safe to attempt to repair the fixture. Much of the wire near the broken portion was brittle, so I knew it would just be apt to break again. So I just took the fixture completely down, capped the exposed wire, and am letting it go at that for now.
I'll be calling a professional to give me an estimate for replacing all the old wiring on that circuit (which seems to be the entire upstairs lighting circuit). We need to install a fan in the bathroom, and it might make sense to combine the projects. If we don't get the old wiring replaced, I can probably install the fan myself, but if we decide to get the old wiring replaced, we'll probably just get the fan installed as part of that.
Anyway, I've sweated enough today. I have a stack of paperwork to get caught up on, so that's how I plan to spend the rest of the afternoon and evening. Maybe I'll grill hot dogs tonight.