Jason, I don't know and I'm surely not an expert on this and have no manual with me (on the road). I'll take a SWAG and hope it helps you though.
Unlike the old defrosters where you turn on the switch and it would just keep cooking, many car manufacturers have come up with ways to limit how long the defroster stays on. People would forget to turn them off and defroster lines would burn open. One very simple way is a timer but that wouldn't do for every circumstance. If you have a lot of ice to melt, the defroster grid wouldn't heat to the point of burning because the ice would be cooling it vs. a very light frost which would be gone in a few minutes. So how long do you set the timer? One setting might not melt all the ice and another might still damage the defroster grid.
So another way is to sense the amount of current draw and once it draws a certain amount of current (draws more current as it gets hotter), a switch would shut it off (in case you forgot to). If that was the case, it could be a faulty switch or a short in the wire past the switch causing it to draw too much current. Either of those scenarios might cause that clicking noise you are hearing.
Again, this is all hypothetical and I have no idea if this is right or not. Just trying to help and it sounded good when I thought of it.

-JoeB