Off the top of my head, I would say that you should feed it from both side brake lights. The sensor looks for a certain current ratio, presumably 1:1 in the case of your wife's car, so splitting the feed should keep it happy. I know that's almost twice the actual work, but at least once you find a way to do one side, the other side should be easy.

You could do the junction in the car somewhere (say behind the plastic trim you can see at the top of the opening when the tailgate is up) so you only have to run one extra wire into the tailgate. Use solder and heat shrink tubing if you want this modification to stay working.

Don't consider disabling the broken bulb sensor.