the radio harness has a switched ignition source and reverse trigger (if it's auto). If not, the cig lighter in the dash is also switched and you can pickup the reverse light wire from the passenger side footwell. I'm pretty sure it's white with a tan or green stripe. I wrote it down somewhere (well over a year ago now).
2012 Deep Cherry Red JKU Sport S - Tickastar, 6 speed, 3.73, Dual Tops