The ignition 12v wire has a fuse blown most likely, recheck your fuses. Fuses F31 (ign 30A) and F41 (Battery 7.5A) in The Central junction fuse box, behind dash panel LH side, may be concealed behind the knee panel.
Get a set of wire ferrules.
Strip back some insulation and use the ferrules as a gauge to measure the thickness of the conductor.
Buy automotive grade wires. In doubt use some slightly larger diameter.
I would suggest that there is a connection between a permanent live and the reverse light wire, probably in the boot area.
This is because :
One, reverse lights usually work only with the ignition on and these are on all the time.
Two, if the false connection was prior to the switch and the switch has not failed, then the lights would go out when not in ...
You have a defective reverse light switch, which is screwed into the transmission. C172 in the image below.
Fairly easy fix to replace it with a new one. Disconnect harness from switch, unscrew switch from transmission, screw in new switch, reconnect wire harness.
NOTE: If this does not fix the issue then it is a wiring problem, the reverse lamp circuit is ...
I only have 2012 info, but perhaps it helps.
However, if only part of a LED lamp is not working, the issue is likely a failed tail lamp assembly, which is probably not easily repairable. Is it the entire running lamp section that isn't working, or just some LEDs around the outside? Do the brake lights and turn signals still work?
Try turning on the ...