I am pretty confident your plan is a solid one. I would do the same thing. Also, if the right side is getting power for the headlight you may even have an easier fix; power from the headlight power.
Unless that is only powered when headlights are on, so back to power from the left side.
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2011 E70 • N55 (me)
2012 E70 • N63 (wife)
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