There's a good chance that it will if all it takes is a wiggle of a wire. Sounds like a bad connection.

 

Just a heads up, it may be a good idea for someone to stand behind the car and you turn the lights on which causes the rear running lights to come on and then you press the brake. If you press the brake, the running light becomes the brake light. Basically there is only 1 bulb which acts as both the brake light and running light. If it stays on and gets brighter you have a loose connection, if it goes out entirely when you press the brakes your ground is loose or not touching. The ground is a small metal tab at the bottom of the socket which can carefully be bent back up to touch the bulb.

 

It's not going to be in the engine bay that's just the main fuses. It should either be under the dash drivers side or on the side of the dash when u open either the driver or passenger door. And the panel you pull of should be labeled and will tell you which fuse is what

 

He's already determined that it's not fuse related, but good idea. You just failed to read his response.