What P0412 usually means
P0412 points away from pure airflow volume and toward the control circuit for switching valve A. That valve is responsible for routing or enabling fresh air during the cold-start event. If the ECU cannot control it electrically, the secondary-air system may never deliver air even if the pump itself is healthy. Common causes include an open coil, corroded connector, failed driver circuit, broken wiring near hot exhaust components, or a stuck valve that has also damaged the electrical side.