Just a guess but as you know, the brake light switch is supposed to supply power to the brake light only.
It sounds like someone has connected the brake light wire to the regular tail light wire so when the switch is activated, it turns on everything.
The first place I would look would be the tail light. The socket should have three wire connectors. One for the tail light, one for the brake light and one for the ground wire.
If someone replaced it with a two wire "tail light only" type connector and then attached both the brake light wire and the tail light wire to one of the connectors, it would do as you say it's doing.
Anyway, somehow the brake light wire is connected to the main driving light circuit and not to the brake light filament in the bulb.