Battery status indicator confusion?

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.

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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.

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In short, don't worry abouth the battery eye.

If the battery performs well, leave it alone. If it doesn't - replace it.