Not sure about other servers, but there are a LOT of people going after the elekks on my server at the time I was trying this. Usually I would have to continue walking around to find an elekk that wasn't currently being zapped. Then I found this little bug...
Basically while you're channeling the zap, simply select another elekk off in the distance. Instead of killing the elekk you're zapping, it kills the one you have selected. This makes a nice convenience for when a lot of people are doing that daily quest (and it pisses people off too).