Ok, I have this all fixed now for the most part. It was a bit difficult to sort out since the lighting isn't done off the battery but off it's own a/c coil.
I found that the solder joints in the high/low switch were broken, which is why I only occasionally had light. The on/off switch had some corrosion, so once that was cleaned I had taillight power. I spent an extra hour or so diagnosing the lack of rear light problem, traced power all the way to the socket, and found that the new bulb was burned out. Apparently, without the headlight the voltage goes pretty high there.
For the time being, the output of the headlamp switch is just plugged into the low beam side of the headlight, giving me a constant light with the engine running. Once I have access to all my tools again, I'll resolder the joints and get the high/low working properly.
The stock style rear turn signals are difficult to find, and prone to being ripped off, so I adapted a different setup:

It's off a slightly newer road bike, but all the wiring just plugged in and worked. It also stiffened up the already damaged rear fender.