The only benefit in doing this is to see if the voltage improves, the problem is this wire gets cooked by the heat from the turbo and so builds resistance over time. You can't use a wire it needs to be a heavy duty cable, i.e. a jump lead, I very much doubt that is causing your problem.

Another way of doing this is to measure the power at both ends of the cable and note the difference!

The light is extinguished by two lives, so for it to come on means the output of the actual unit is dropping, when you apply the brake lights that is circa a 3.5A load, switching on the heater, headlights etc should produce the same result... so it's either a bad unit or a bad ground connection.

Martin