2002 TB LS, you are missing an important point. First, you have to install a new connector onto the factory wires that go to each headlight bulb. Then you plug the "heavier duty wiring with an outer protective layer between the new connector on the factory wiring and the headlight bulb.
NOTE: The product I suggested is not just insulation. It is heavier gauge wire with heat resistance insulation and heat resistant connectors (they should not melt unless there is a fire) that tolerate the environment better. They sell for about $7.00 on rockauto.com and considering the cost of wiring pigtails and connectors these days, that is a darn reasonable price!!!! I spent $25 dollars for a 4 inch section of 4 wires with two connectors (one old style and one new style), so $7is a steal!