I don’t understand. The lights in the rear come on when the headlight switch is off? and goes off when the headlight switch is on? The taillights work during the day but not at night?
Engine running, headlight switch off
Taillights on or off?
Engine running, headlight switch on park position
taillights on/off?
Engine running, headlight switch on headlight position, brakes off
taillights on/off?
Engine running, headlight switch on headlight position, brakes on
taillights on/off?
brake lights on/off?
BTW, the fuses and the headlight relay should be in a fuse box under the hood, usually near the battery.