It's completely normal for voltage to fluctuate based on engine load. If the car needs more power (such as during acceleration), it may dial back the charging voltage. If it has power to spare, it will take the opportunity to charge the battery. You might want to study it in that light.the battery voltage weirdly fluctuates from 12.0V to 14.0V with no evident correlation to pedal input, engine revolutions, idle, etc. It seems to be acting on a mind of its own.
That said, bad battery ground cables are common. And any corrosion should also be addressed.
Also, be on the lookout for any devices that connect directly to the battery. The car monitors battery current and incorrectly installed add-on devices might fool the system into cutting back the charging voltage.