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I know you said that you wanted OEM, but I went with one of the strip kits that are sold on Amazon. I did exactly what you plan on doing. I ran two 12ga wires in plastic loom from the battery along the right-side frame up and into the rear of the bed. I ran the wires up and drilled a cutout in the right-rear OEM bed light knockout. I then made my connections and tied everything up between the bed liner and bed wall.
I attached the light strips to the "lip" of my OEM bed rail covers and the switch is right above my right-side Swing Away box.