Hi percypig and welcome.

The Power Indicator light illuminates in green while the computer is on, blinks slowly in orange while the computer is in Sleep mode, and turns off when the computer is turned off or enters Hibernate mode.

It is always on when the computer is on - using AC or Battery.  Are you saying it stays on even when shut down completely?  If it is still illuminated when the Vaio is shut down and disconnected from the AC, then you have a fault and will need to speak to Vaio support.

Which model do you have?

Light indicator still lights up since it is still getting power from the battery when the power adapter is disconnected.