If the alternator is not charging then I would recommend doing a voltage drop test across the battery cables to see if one of them has high resistance.
Take a digital volt meter and probe the positive battery terminal with your test lead and probe the battery cable at the alternator with the other lead and measure the voltage. Move the test lead to ground terminal at battery and the other lead attach to the alternator housing and measure that voltage. Both tests are with your vehicle running.
I have included example images below. Those test are for a good vehicle. If you measure say 2 volts across the ground cable then you have high resistance on that cable and you need to check for a loose cable or corrosion. And also very important, make sure the battery terminals and cables are clean and free of corrosion. Let us know what you find.
Images (Click to enlarge)
Sunday, December 22nd, 2019 AT 4:51 PM