As a former mechanic, I can tell you that splicing wires is not really desirable. The splices can work loose and cause major headaches when you're trying to diagnose future wiring issues. I have worked on many vehicles where the owner had wired accessories by splicing into existing circuits. It can be a nightmare.
As previous posters have suggested, first find out if you have a voltage issue or a moisture issue causing corrosion or shorting. I would recommend replacing the converter instead of rewiring it. They're not that expensive when you compare the cost of fire damage or burned up wiring caused by a bad wiring job.
