Short in the wiring, or the circuit is overloaded.
in the fuse box under the hood
Yes
As far as I know, they are not on the same fuse/relay.
There is a short in the wiring or a corroded brake light receptacle.
It's in the left engine compartment.
The brake light fuse, the courtesy light fuse, the cigarette lighter fuse, should all be hot with the key off.
You need to CHECK the brake light FUSE with a test light. If the fuse is okay then check the brake light switch. That is just above the steering column under the dash. It is H..L to get to.
Check the fuse, check the bulbs, then check the brake light switch.
Read your owner's manual.
The 1997 Pontiac brake light fuse is located in the fuse box. The brake light fuse will be labeled as the tail light fuse.
Check the bulbs, Check the fuse, Check the brake light switch, in that order.