12.6 volts for a 12 volt battery is fully charged. It will likely be higher right at the end of charging. I don’t think you have written what the voltage is with the batteries combined into a bank. Your charger is sensing that and seeing that voltage as charged. My chargers are free when they aren’t hooked up, so if something is wrong with the pack connection and your voltage is zero you might get a green light then as well.
You began by saying the bike stopped after a few blocks? If your bank of batteries are coming out to 60 plus volts it’s not the batteries. And the scooter likely anyways would run on lead acid way lower then you ever should discharge them because, as far as I know, only lithium batteries have battery management systems (bms), so there is nothing to stop it from discharging to zero, (if you every left a light on in your car and came back in a few weeks later you know what I mean). You need to follow your wires and test at every junction, or start at the motor and see if the voltage is getting to it. Then see if it is getting to the controller. Then work back to the battery checking for maybe a fuse or a switch along the way. Also, if you have any safety power cutoffs such as brakes, make sure those aren’t activated.