It looks to me like it has a wire heading up to her hair, then probably to her hair-covered ear, but another thought I had when I saw it was that it was some kind of electro-shock contraption, and that Huma or someone like that black "Doctor Diazepam / SS agent" had a remote control device to activate the shock (or diazepam injector) whenever they saw Hillary getting ready to faint, wobble around, collapse, or have some kind of seizure.
It kind of looks at one point in the debate that she gets some kind of shock which causes her to start doing a shivering shimmy move, with a big goofy smile on her face (similar to the odd smile she displayed when she had that famous head rolling/wobbling episode).