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Most likely the brake light switch is bad. Look under the dash at the top of the brake pedal and you will see a switch that gets pushed when the brake pedal is applied.
Unplug the connector and jumper the 2 wires that you unplugged together with a paper clip or a small piece of wire and see if the brake lights come on. If they do, replace the switch.
The reverse lights are on a different circuit and they get power from the neutral safety switch on the side of the transmission (if its an automatic trans)
Have you had a chance to jumper those 2 wires?