I worked on cars where the switch was out of adjustment on the column allowing the contacts to make a slight powe feed , but also I had alot of the cheap alternators have bad bridges or regulators in them ( they will still put out a full load but not a full wave ) , pulling the wires on the alternator overnight is a quick cheap check for that .also charge the battery up to a full load before testing everything , you should run the motor above 1000 rpm over 10 minutes to fully charge a battery after starting ( at idle it will cut out charging as the speed is not fast enough at times )