To diagnose that fault code it is important to understand what the system is and how it works. It is NOT an EGR system. It is an air injection system which injects air into the exhaust flow for about 2 minutes or so after starting a cold engine. That extra air (O2) allows the cat to start working sooner thereby reducing emissions during warm up. You should hear the pump motor run shortly after start up. Does it? If not is the pump motor good and do you have power to it? Sometimes the motor seizes up. Remember it is only activated for a short time on a cold engine, not after a warm start.

The system will periodically perform a self test while you are driving and engine is fully warmed up. It starts up the pump while you are stopped at a light with engine at idle. During this short test the O2 sensor will sniff that there is extra O2 in the exhaust and tell the computer that all is OK with the system. This test is only done once during a trip and maybe not on every trip, not sure. If the test fails you will get a code 410. Possible and typically this a leaky vacume line from the the solonoid activated valve to the vacume operated air injection valve on the exhaust side. That fault will not prevent the pump motor from activating though. Do a cold start and check for vacume (while pump is running) at the end of the vacume line at the injection valve.