The harness should fix your problem, with the harness you'll be getting power directly from the battery, and the stock wires are just providing an "on/off" signal to a relay. This means your stock wires will be pulling very little current. If you still have problems once you install the upgraded harness, start looking for a frayed wire that is shorting out.
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'99 GTP, L36 bottom, XP cam, Headers, 3.29 gears, FWI, Powrtuner