You are correct in that you can use a thicker wire to provide a power feed, to connect to the aux light original wiring harness.
Just make sure that your joints are good and are properly instulated plus weather-proofed for when exposed to the elements. Insulation tape simply don't last. To weather-proof the connections you may want to use heat-shrink tubing on each individual connection plus cover the complete joint bundle with a second layer of heat-shrink tubing
Also make sure that the heaver guage wire and the joint is adequately supported as not to cause the any weight of the thicker wire to cause possible problems do to constant vibration, etc.
