Headlight Wire Corrosion Options

[gwena4]

The passenger side headlight on my 2003 Corolla went out about a month ago, I replaced the bulb but that wasn't the problem. The light will come on if I press in on the wires going into the casing. It looks like one of the wires is exposed and corroding. I poured some Coke on it, and that ate away the corrosion, but the light will still only come on it I press in on the wiring. Do I need to wrap the exposed wire in electrical tape? Could it be a grounding issue? Thanks!