To be honest, only one of the two witches is blinking. I somehow managed to break the other one before even getting to wear it. Disappointing, that... but I guess this is what you get for $3.99 worth of blinkingness.
I thought I'd try taking it apart and fix it. By "fix it" I really mean jiggle it or poke at it until it either starts working or breaks further.
I am reminded of a time when I was a teenager, driving my mom's car somewhere with a friend. We were about to head home, and the car wouldn't start. Neither of us knew anything about cars beyond where to put the gasoline, but we popped the hood anyway. We both stared at the engine hoping vaguely that there would be a big wrench sticking out of it, or something equally obvious. There wasn't.
It turns out with the car that I'd accidentally left it in Drive. Cars (or at least that car) don't start when not in Park.
With the earring, it turned out that my little computer screwdriver was not small enough, so I wasn't able to take it apart nor fix it. I'm just wearing the non-blinking witch on the left, because nobody sits to my left at work.