My preferred method to tap into wires:

Use thermal tweezers to remove the insulation. The strands of wire have a natural twist. Untwist them just a bit so that the strands can be separated into two halves. Take the new wire, run it between the two separated strands. Twist together. Apply flux. Apply solder. Nice connection that doesn't pull apart! And the best part is the original wire isn't cut. And although I've never had to test this, since the wires are never cut, then the car is still under it's full factory warranty.

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