Check volt meter on another battery if possible.
Hopefully it is off
11.9v means battery is bad.
A Car battery has 6 separate cells inside, each will have 2.15volts when new
6 x 2.15 = 12.9volts
So new battery will show 12.8 to 13volts
at 5 years old it will be down to 12.3 to 12.4volts, cells lose volt and amp storage as they get older
At 12.2 volts and under battery will still start engine but is fading fast, if engine doesn't start first time cranking you probably won't get a second chance, and on a cold morning no chance at all.
No, the 11.7v on green wire is OK if battery voltage is 11.9v, there will be some loss on that circuit.
With key on, Ground the green wire, battery light should come on.
Then put a jumper from yellow wire to green wire, Battery light should go off.
If it does then voltage regulator in alternator is the most likely problem.
Battery light works this way:
A light bulb lights up if it has 12volts on one contact and Ground on the other contact.
If you put 12volts on both contacts the bulb will not light up.
When you turn on the key the Battery light gets 12volts on one contact, dash power.
The other contact is the green wire at the alternator.
Alternator is a Ground when it is not spinning, so battery light has 12volts and a Ground, it lights up.
When alternator starts spinning it is now 12volts(14volts) not a Ground, so battery light goes off.
There is a little more to it in that, the green wire supplies the initial voltage the alternator needs to start generating its own voltage, that's part of the voltage regulator circuit, which is most likely your problem.
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