Sounds as if the wires at the rear of the vehicle are mixed up. Check to see if the brake lights come on when put into reverse gear. That will rather confirm the hosed wiring.
Fog lights are in the front; they are commonly referred to as "brights" because they are the brighter of the two standard headlights. Brake lights are in the rear; they light up when pressure is applied to the brakes or when the car is in park or reverse.
shift position sensor failed, or wires are shorted
to warn the drivers behind your automobile that you are slowing down
If the back dash light will light when the brakes are applied but the two tail lights will not light up, there is probably a short in the wiring somewhere. It could also be that the fuse for the brake lights is burned out.
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.
Someone may have switched the sockets in the back of the lenses.
Bad ground, usually at the rear lights.
Most probable a broken bulb somewhere.
If you just barely touch the brake pedal the brake lights will come on but the brakes will for all intent and purpose not be applied.
There probably is only one cause for your interior lights to go on when you apply the brakes. There probably are brake light wires and interior wires that have warned together.
Where is the fuses for the brakes lights Buick Rivera 1970
Where is the fuse located for the reverse lights