I will assume you have the 4Y engine.
That "Thing" next to the distributor is actually a part of the distributor (As seen in the photo provided of a brand new assembly).
I have two Toyota 42-5FG25 machines at my site too, and both of them have this spare wire that seemingly leads to nothing.
I've always been curious too, but I have two reasons to believe that it's nothing to be worried about.