It's a common problem, with the heat the cable builds resistance, not to mention the age factor!

There is nothing wrong with the power you have, even with a new cable I doubt the two will marry exactly, due to the resistance of the cable.

The cable runs directly, it is on ERST's it goes via the starter.

As said the problem with the light is caused by unequal power (it doesn't really tell you much to start with) basically your probably getting less power on the ignition live side of it than on the alternator side, hence it illuminates.

There is another problem where the power drops to the car side, it's worth checking the voltage at the ECU...

Martin