I HAVE A 2005 3.3

egr valve replaced and check engine light comes back on with p0405-check wiring at connector-if ok try performing at battery static discharge-disconnect both battery cable ends-and touch cables together-this discharges all ecu capacitors and resets adaptive memory

Its the solenoid controlling the EGR valve movement that is likely at fault. if theres a vacuum pipe running from the EGR valve it goes to a solenoid that opens and closes the valve. If it just has an electrical connector on top of the valve, the solenoid is built in. If its built in you probably have a wiring fault at the connector or in the harness to it.