This indicator is almost pointless. The only reason it exists is that is increases sales of new batteries.
Translation of colors:
Green: electrolyte is dense enough (battery charged above some point) and high enough level.
Black (white on some brands): electrolyte is watered down (battery somewhat depleted) and still high enough level.
White (red on some brands): electrolyte is low. May need topping up with deionized water (but the battery is likely marketed as maintenance-free and hard to open, so no topping up possible).
The green color may be a matter of mixing the electrolyte. A fully charged battery turn green only when shaked.
The level somewhat depends on the temperature, a hot battery may have somewhat higher level.
Whatever the indicator shows, it is immersed in one cell, others (esp. in older battery) may be in another state.
The voltage of the battery (with no engine running) is pointless as well.
Less than 12.0V - battery depleted or bad
12.1..13.0 - battery MAYBE in some state of charge other than completely depleted.
Above 13.1V - battery in some rare failure mode with voltage above normal, no good behavior expected.
One cannot deduce a state of charge of a lead-acid battery by its open circuit voltage, other than to distinguish between completely depleted and somewhat charged.
In short, don't worry abouth the battery eye.
If the battery performs well, leave it alone. If it doesn't - replace it.