Brake light does not work

I found this useful diagram at troubleshoot vehicle.com. It answers your question. Fuse box is located below steering column.
Driver Side Fuse Panel
(1993-1996 Toyota Corolla) December 21, 2013 Updated: December 21, 2013 Written by: Abraham Torres-Arredondo In the table below you'll find the fuse location and description of the fuses of the driver side under-dash fuse box on 1.6L and 1.8L 1993-1996 Toyota Corolla.
The fuse box is located on the driver side of the dash, below the steering column.
1993-1996 Toyota Corolla Driver Side Fuse Box Fuse Fuse Name Amps 1 Cigarette Lighter, Digital Clock, A/C System, A/T Shift Lock, Alarm, SRS Airbags 20 2 Tail, Parking & License Lights, Instrument Panel and Daytime Running Lights 15 3 Fuel Injection, Cooling Fans, Battery Discharge Light 10 4 Cruise Control System, Daytime Running Lights 10 5 Fuel Injection System 7.5 6 Stop Lights, Cruise Control, Shift Lock System, Anti-Lock Brake (ABS) System 15 7 Turn Signals, Emergency Flashers 10 8 Starting System, Anti-Lock Brake (ABS) System, Shift Lock System 15 9 Gauges, Reminder Lights, Back-up Lights, A/C System, Daytime Running Lights 10 10 Front and Rear Wiper/Washer System 20

check tail , brake and courtesy fuses , in engine compartment fuse box , and driver side fuse box under dash

Hello, welcome to FixYa.

The fusebox for an 03 Corolla is on the driver's side of the dash, above the plastic panel that is above your knees. You can see it by looking up and to the left, under the instrument pane, with a flashlight. It is a rather large white or cream-coloured box (depending on where the car was produced). An easier way to get to the fuses would be to remove the plastic trim panel that is directly under the bottom of the instrument panel.

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Pop the trunk.

Look at the backside of the tail light area – it’s wide open. Turn the affected light bulb socket to the left. It’ll take some force, but you won’t break it.

Once it unlocks, you can pull the light bulb out.

Push the new bulb in.

Put the socket back into its place by pushing it in, then turning to the right. It’ll lock back into place.

Test the brake light to make sure it works.

Brake light fuse , or burnt out bulb , or switch on brake pedal.
The bulbs have 2 filiments in them , 1 for running lights and 1 for brake lights.

you have to go from the inside the trunk some the bulbs are there others there will be nuts there to remove the tail light to get to the bulbs

Try cleaning the contacts with a wire brush if they appear dirty and then apply a small amount of silicone to the bulb contacts also try replacing the bulb as sometimes they don't appear to be blown but are

check under the dash on the passenger side. or up behind hood release lever on the driver side.

Could be a bad relay switch contact. Or bulb contacts. Remove the bulbs and check it with a 12V test light. Aligator clip to any ground and touch the contacts inside the bulb socket.

Is there power to the bre light switch, a 12 volt test light works gret for this test, they are cgeap and avail at any parts store. If the switch has power in and out when the brake pedal is pressed then the turn signal/multifunction switch is most likely the problem.