for a long term repair. go pick up some flux core solder, 3 bucks at the shack, and some shrink wrap tubes, another 5, then use a lighter if you dont want to spend money on a soldering iron, heat the wires touch the solder, it will flow over the bare wire, let it cool, slide the shrink tube over the solder, heat it up with a lighter to shrink it. it will be a strong weather tight connection that will last forever. put the shrink wrap tube on the wire first, when done soldering slide it over the splice. when its cold, if its warm still the tube will shrink and not fit right.
taping it will fail by next year.