Which wire is suitable for connecting runs of EL wire?
Thin wire is fine. El-wire actually works as a giant capacitor which is why there's hardly any current flow. If you look at the ends of el wire, you'll see that the wires themselves are very thin. That's both the core and the outside wire. The thicker your connecting wire, the better off you'll be, but you should be able to go very thin, at least as thin as the actual conductors in el wire.