Yeah, it sounds like your battery is about to die and can't keep up with the load, why, probably due to voltage regulator is failing to.
You know when you charge the battery and the charger shows it's fully charged, that doesn't mean it's fully charged. If you have the kind that has caps, take them off and get a "hydrometer". If you don't have one go get one! It's important because a hydrometer tests the specific gravity of the battery acid. All four colored balls floating, battery full, only three balls floating 75% full, two colored balls, 50% and so on. If there is one or two or three cells that don't have all four colored balls floating, keep the charger on the battery until all six cells a full up! This can take up to fourteen hours to arrive at. Then the battery is fully charged. As for the alternator, the voltage regulator may be weak, change it out. And folks, rebuild your own alternator's! There's no reason to go buy a new one when it might only be a diode trio that's bad or the voltage regulator. They aren't hard to rebuild and the internet is full of all kinds of tutorials, maybe even right here on this forum. I've not looked so I don't know. I've been rebuilding mine since I don't know when, decades.