Trailer battery recharge by towing vehicle. Connection?

Hello It is about charging a trailer (kipper) through the towing vehicle. The trailer has its own battery for the hydraulics of the pump. The pulling transporter is normally connected by power line (normal trailer light) with the trailer. Supposedly it should go through the normal trailer light box to charge the battery of the trailer. Unfortunately, this is not possible at the moment! The trailer also has an extra connection for 12 V, for the battery of the hydraulic pump.(I think) If m on the battery of the trailer just 12 volts from the battery of the transporter, then this would be charged, but what would happen if the battery is fully charged, and 12 volts is still on? Wouldn’t one use a charging current controller for it? Is that just so? Could I turn off from the transporter connection box (light trailer), 12 volts and put on the battery of the trailer. Or is in the connection cable (light trailer) already a wire reserved for s owhat?? Need to know this urgently! Greeting G2s