Thanks for the input, Russel.
In another thread here, mike said that Woodbabies use
flexible pushrods meant for model airplanes. I've seen Woodbabies in videos and they seem to have no trouble with both twisting and nodding motions, so if the bike cable doesn't work I'll try that. At this point I'm just experimenting with the mechanics and I really can't afford the best materials, but I'm taking notes for later.

I ordered a cheap brake cable on Amazon, it should arrive in a couple of days. I'll let y'all know how things turn out, with pictures when I have some.
On a different note, another method of making a ball joint occurred to me, similar to Shawn's paper mache method. If you made a ball and socket from clay, you could make them hollow and poke holes in them to string elastic through. Then you wouldn't have to deal with keeping the pieces together as much. I haven't gotten to try it yet though, and if you can get a suitable ball making the socket from paper mache like Shawn did would most likely be better under most circumstances. Just thought I'd share anyway.

EDIT: Forgot to mention, this is going to be a rather small puppet, so flex conduit would probably be overkill for me. My first model will be a small bat-like creature, only around 8 inches tall, with the only articulation being the simple bend and twist in the head. The brake cable should be enough for that, but like I said above I'm taking note of all the materials mentioned. It might come in handy, and I also enjoy seeing the things people can make out of everyday objects. :D