why does my brake lights not work when my headlights and taillights are on?
Most likely your bulbs are older and the filaments are weak. I would suggest trying new bulbs first. It would be the first in eliminating that. If you have already changed the bulbs recently and KNOW they work, it is possible that your connections are corroded and need to be cleaned. You can purchase electrical connection cleaner to remove oxidation etc. Then, use electrical connection grease, available at most auto parts stores to ensure corrosion and moisture are kept out.
Nothing to do with "weak filaments" ... these are the classic signs of a lack of earth capacity. Main lights are taking up all the earth capacity. Clean earth wire connections and ensure bulb bodies and holders are free from corrosion.
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