There are several fuses relating to the lighting. The fuse panel is at the left end of the instrument panel (drivers side). Open the divers door and look about armrest high to locate the fuse panel cover.
I would check the running lights for one with a short. I had the same sort of thing with my trailer and I spent way to much time troubleshooting the brake and signal wires. Turns out a running light bulb connector was grounding out on the trailer and messing it all up.
The whole turn signal arm unit needs to be replaced
A TNS relay is located in the fuse box of a vehicle. It controls the vehicle's turn signal lights, running lights, taillights, and dash lights.
If all the running lights (front & back) are not working I'd start by checking the fuses then onto the headlight switch
to differentiate it from a brake light or running lights. Its the only one that BLINKS at a regular rate when looking at it from the back.
signal lights not working.
Be sure to keep the rear tail lights, brake lights and signal lights in good working order. To many times you see vehicles with lights missing.
Basically, it comes down to the year of the vehicle, and whether it has "City" lights. Running lights (a.k.a. daytime running lights) can be an intergal part of the headlight bulb, meaning that it's the same bulb, as your low beams, just lower voltage signal. With city lights, you need a different bulb. Refer to a Repair Manual (I prefer Bentley [TM]).
There are separate fuses for trailer signal lights in main fuse panel
GET THE POS AND NEG WIRES AND RUN THEM TO YOUR CORNER LIGHT'S NEG AND POS WIRES.
have your day time running light module checked the same thing happened on my car
The only thing that will work with key OFF is the brake lights,head lights and emergency flashers. Dome light will also work.