What P0405 usually means
P0405 narrows the EGR story to a low feedback signal on the valve-position or related EGR sensor circuit. Depending on design, that can mean the position sensor is biased low, the signal wire is shorted toward ground, the reference voltage is missing, or the valve is physically parked near one end of travel in a way that makes the low signal believable. The key is not to assume the sensor alone is bad until the whole circuit has been checked.