OK, now I get it (looked at the online manual). The connections are inside the AC Junction Box and you removed the cover plate. If the wire nuts are installed properly and there are no loose strands sticking out, then there should be no shorting. Unless the insulation on the wires has been damaged/compromised. If the electrical tape truly covered the damage, it should not have shorted out.
There's probably not enough slack in the wires, but at this point, if there was, I'd try cutting back the wires from the wire nuts and reconnecting them with new wire nuts of the correct size. My guess is the connections in the wire nuts are the problem since that seems to be where you're describing the damage.