The LS ECU will manage the alternator for you. You can leave 4A hanging (taped off or de-loomed), then just not worry about the voltage sense wire on the left connector in your picture.
Edit: The LS harness will have ignition switched power. Depending on how it is set up in the painless harness, you might be able to use 4A to feed it.
You will still need the large wire from the alternator to the battery/starter. It is likely that it should be thicker than the AAA harness provides because the LS alternators were higher current than most any of the stock older ones.
Last edited by Fibonachu; 08/19/2024 4:27 AM. Reason: Add detail