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The wires were melted beyond just cleaning. Had to replace them but unaware which wire is connected to them both are yellow with no markings. I am assuming that it doesn't matter which one to reattach to.Agree on yellow being battery charging. For some reason, these connections tend to absorb moisture and corrode even though they are encapsulated....to a point. Corrosion in connections represents a resistance to current flow and with current flowing through it generates heat. Heat melts the plastic.
If the charging circuit still works, either disassemble the connections and clean away the corrosion, or replace them. You're not the first person to report this problem on this site, or others.