First thing to do is clear the code and see if it comes back on again.
The ECU continuously monitors its own internal memory status, internal circuits, and output signals transmitted to the throttle actuator. This self-check insures that the ECU is functioning properly. If any malfunction is detected, the ECU triggers the P0605 code and brings on the EML.
Possible causes:
ECU may be faulty
ECU harness power supply circuit is open or shorted
ECU harness ground circuit is open or shorted
I had a 350Z in last week with the same issues and the ECU was fooked due to water ingress as the bulkhead power harness grommet had not been refitted properly and water was dripping onto the ECU.
Preowned ECU's in stock for a few 350Z applications.
Just drop me a PM if I can help further.
Alex.