[VetteVet]

I would take a look at the brake/ turn signal wires, in the harness from the firewall to rear lights and the front turn lights wiring. These lights are exposed to the elements and may have been shorted by the moisture from the heavy rain. Also check the lights themselves for any water inside the lenses.
The brown tail light wires might be shorting the yellow or dark green brake light wires at a break in the insulation or at the lights themselves and causing the lights to come on.
The harness connector at the rear of the truck would be suspect for that.
Good luck.