Brake light and tail light are generally separate circuits so for both to fail, unless the wiring is damaged (where it passes over or under the rear mudguard is usually vulnerable) it is likely something they both have in common and that is the lamp, often the bulb and the ground or earth...
An indicator flashing faster than the other side suggests that side is consuming a different amount of current and that can be caused by fitting a bulb with a different wattage or by a poor contact somewhere including a poor ground.
Look at all the bulbs first making sure they are all clean and correct and the bulbholders are also clean and working correctly. Using a test lamp test the supply to each bulbholder using an independent ground.
If all is correct it would seem to be the ground that is defective.
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