For the brake lights, I'd test the switch next. Use an ohmmeter (ideally one that beeps on electrical continuity) to probe the outputs of the brake pedal switch.
You'll need to disconnect the cable from it first. Once you depress the brake slightly, it will release the switch (it's a normally closed switch), and you should read contact between the two pins.
Not sure about the headlights. It sounds like there may be a problem with the wiring, either a short or a break. I'd do a voltage test between the pins and ground while the switch is on. See if you're getting anything at all. One of the pins (the gnd) should make contact with the car body. If more than one make contact with gnd/body metal, there's probably a short. If none of them do, then there's a break in your ground wire.
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