JD LT133 charging problem

The battery isn't charging on my JD LT133. Upon investigation, I found a broken black wire coming off a four pin connector. I think (guess) it's coming from the voltage regulator, it splits into a two wire (black and yellow) between the engine and the connector. When I touch the black wire to it's broken connector it archs even though the mower is off.



I think I should just disconnect the battery and repair the connection. Any advice?