Check the trailer light connections.
Fuses
have you checked the fuses?
have you checked your fuses?
The light switch.
Next step would be to check the fuses
Check the fuses and if they are good then check the brake light switch.
If the parking/tailight fuse is good - then it may be a bad headlight switch No tail lights but the bulbs are working? Please explain.
I'm thinkin' the headlight switch is at fault.
Check the bulbs - they are doubloe filamented with the smaller being for brake/turn signals Check the fuses
Check your fuses. See owner's manual for location and assignment of fuses.
Perhaps something in the gear shift that turns on the lights when in reverse position.
check fuses , daytime and lights on use diff fuses.