I replaced the bulbs and inspected the sockets. All good.
I checked all the connections in the rear of the car and everything seems fine there. And all the Earth's look good to. I checked ohm readings from earth in the socket to the frame and that is good.
When I have both bulbs out I checked the sockets with a meter, and everything there is working properly.
The issue is when the side lights are on and the brake pedal is pushed. It must be a problem with one wire somewhere, but I haven't found it yet
Despite your tests with a meter, I would still suggest that you get a long piece of insulated wire and connect one end directly onto the earth terminal of the battery. Then attach the other end directly to the body of the brake light bulb holder on each side and see if it makes a difference.
