Yep, that was the problem....the hose had gotten knocked loose somehow. I found it, reconnected it, and the windshield washers work just fine now. The fit wasn't all that tight, so I may look into gluing it or something later - but I used the washer a few times and it stayed on, so I'll leave it alone for now.
I think I also located what must have been the pump for the headlight washers, it was on the other side of the tank near the outer body panel. Strangely enough, I didn't see a hose running up to it, or even a place where a hose could have gone - but the view was somewhat obscured and I didn't have a flashlight. It'* not that important though, so I'll mess with it at some other point. I thought I noticed just a little bit of the fluid on the ground, but that may have already been in the parking space when I pulled up. In any case, the fluid wasn't draining out like it had been before, so I'm happy.
Now, if I can just manage to install that O2 sensor I've ordered without destroying anything... :P