To the moderators, if I have should replied instead of answering, I'm sorry I was about 1200 characters short and this is my first post and I believe it can will help people finding their way if they have the ABS and battery light lit
Thank you for your answer. I've had no experience with alternator voltages, but I measured 12.4 volts when not operating and 12.3 volts while the engine was running.
I also checked for the alternator belt if it had enough tention and it did.
While I suspect now that the alternator is going or already gone, I did check the fuses and all seemed okay. However I was able to lookup in a service manual for this model (Nissan B13), and it had an diagnostic procedure. While I first did test my ABS by breaking hard enough, I wasn't expecting this would be a valuable clue, since the diagnostic procedure stated that if the ABS light has come on, I should check the diagnostic LED for flash codes, but the diagnosic procedure mentionend a burning ABS light, together with working ABS when braking, with no flashes of the ABS management computer LED, it said it would be a faulty alternator. This LED did flash once when I turned the ignition, so I am sure it is a working LED.
All in all I have found two clues, a too low voltage while the alternator is running and a diagnostic that ABS is working and no LED flash code it is saying faulty alternator. I'll now start looking in to looking for a second hand, or repair and replace.
I want to mention this is an OBD (OBDI) car, there are no fault codes from OBD I know because I use Nissan Datascan (however I didn't check for it either) but then the service manual would have pointed to the Nissan dealers testing computer.
I am happy with your answers since this gives me more confidence to repair it myself, I am not aware for my Nissan of grounding the L terminal, I also don't know if it is on my car or not and the engine's management computer, OBD connector both have no LED, just the ABS computer has a LED.