Tail lights and license plate light out on 2013 f150

Bad ground

If the turn signals and brake lights work, I would start by checking the bulbs and sockets pay attention to the brown wire and if all else is OK follow that brown wire underneath the truck look for connectors that are badly corroded or a broken wire. also check the tail light fuse.

Highly unlikely that 4 light bulbs would go out at the same time. 90% of chassis electrical problems are on the ground side. Common denominator for all 4 lights is the ground.

Check your fuses.