Fuse 32 (TBC 5) in the rear fuse block is the only fuse associated with the reverse lights.
The reverse lights turn on via a driver in the BCM. If this wire was shorted, like when a live loose wire hits a metal kick panel when wiring up a reverse light box, you may have wiped out the driver. The service manual does not mention if the bcm will turn off the driver/set a code if it detects that the wire is shorted. It says that if you have no pcm dtc's, have a ground at the reverse socket(s), and have continuity from the bcm E5 (light green) to the positive at the reverse socket(s), then replace the bcm.
But before you do any of that, I would triple check that fuse first (12v on both sides with the key on), and then try to reset the bcm by cutting power to it for a 1/2 hour or so.