K12 Rear lights not working properly.

Hello, my Wife has just got a K12 Micra.
It has rear light problems, when you put the lights on with the indicator the number plate light flashes and when you put your foot on the brake pedal the indicators flash very fast.
Was thinking earth, but the plugs and earths look fine.
Have heard about running a separate earth wire.
Any ideas would be great, thanks.
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My right rear light, (passenger side), was acting weird, turn signal was dim and when using it, rear driving bulb was also blinking dimly.
I added ground wire and after that everything worked normally.