Has a Tech2 been used to see what is in memory?
Are the instrument lamps the only lamps lighting up?
No others, some of which could be usually switched off, eg AC / Fan switch, CD player/radio aerial, rear reading lamps, dome lamp, and others out of sight eg. glove box lamp, and then unusual lamps such as hazard switch illumination, tailgate illumination, fog lamps, Head Lamp Switch, stop tail etc. are lighting up?
Have you tried pulling each of the fuses under the dash in sequence, and observing if the problem changes/disappears under certain fuse removal conditions. If it does, it could indicate a pinched wire in the wiring which is supplying a 12v feed or voltage to the incorrect circuit when the brake's applied and or gear selector lever is moved to reverse etc.
Has the filament in a stop/tail combo bulb blown and cross feeding the circuits?
Referring to the Haynes 41743 manual. (I have some reservations with accuracy, but as they say, that's all there is apart from other third party manuals which have been reported as not accurate also).
This interpretation is my take. Haynes shows on a schematic that the Reversing lamps relay is located under the bonnet (?). I think it is in the BCM. (Someone on the site can clarify this please?). The schematic shows it is operated by the PIM computer for the 5 speed auto, and for the manual transmissions by a hard contact, presumably in the transmission housing.
The footbrake lamps are associated with the ECM on the V6 and wiring wanders off to other circuits.
I notice you have a trailer harness, is this factory supplied and not modified, or connected to an adapter socket for after market purposes? In my sedan the trailer loom sits with the spare tyre in the boot floor well. Could the wiring get pinched under the spare tyre at any time and caused a pinch/burn through? Moving the trailer wiring around while testing might be worth a try, as there may be a pinched wire in the wiring loom etc that is back feeding the vehicle's wiring.
The trailer wires appear to be connected to the BCM and the ECM as much as the high current lamp assemblies.
Right flasher BCM, Left Flasher BCM, Reverse seems to go to high current lamps, Stop lamps to ECM.
Hope this helps.