The "brain box," more accurately called the
Powertrain Control Module (PCM) or sometimes the
Engine Control Module (ECM), on a 1996 Chevy Cavalier is typically located
under the hood, near the firewall. It's usually mounted on the inner fender well, often near the battery or other engine components. Its exact location can vary slightly depending on the specific engine and options on the vehicle.
To find it, you might need to look carefully – it's usually a fairly sizable, rectangular black plastic box with numerous connectors. A wiring diagram for your specific Cavalier's year and engine would be very helpful in precisely locating it. You can find these online through automotive repair websites or manuals.