yes they should
In the back should be tail lights which always come on when the headlights or parking lights are on, and stoplights which come on whenever the brakes are pressed. The stoplights should be brighter than the tail lights, but they should be separate.
The brake lights.
Probably a faulty brake light switch or the brake light switch is installed incorrectly.
The rear brake lights.
wrong bulbs or bad earth
In the state of Arizona cars should be sold with working hazard lights, but there is not a law stating that if the car is sold without them that it is illegal.
The red ones in the rear of the car. Note: They are separate from and next to the red lights that are on constantly when you turn your head lights on.
Check the brake light switch it's self, it should be on the brake peddle arm or bracket. The switch should show open when the peddle is neutral and should show closed when the peddle is pressed. If the switch shows nothing either way then it's hooped.
Check to see if the stop lights are working - shift interlock and stop lights should be the same circuit - check fuses Try turning the key to 1st position (unlock) Shift to neutral to start and then shift to Drive
nothing it could just be the tail lights coming on.
My Brake tail Lights Stay on when my car is complete turned off and my lights are off to.
There is no switch to activate or deactivate the brake lights on a 1988 Nissan. The brake lights automatically turn on any time the brakes are pressed.