Does the Charger start (fans spin up)?
12.6V means nothing as under load, even a small load it may break down and drop a lot lower.
A lead acid battery is made up of 6 * 2V cells one or more may fail under a small load dropping the voltage below that required to activate the the charger relays.
However having said that, can you still drive the car without the charger plugged in? If the charging relays do not activate then the Car thinks the charger is not connected to the supply and acts as normal. This would concern me as the 12V battery also activates the traction battery relay and therefore should have enough power in the 12V battery to activate the charger.