The operation of the the air injection system occurs for about a minute and a half right after starting a cold engine. It pumps air into the exhaust system to start up the chemical reation in the cat a bit faster, then it shuts off never to be used again until the next cold start. But....the system gets tested occasionally during driving when you are at idle (if the idle period is long enough) the pump starts up and the ECU checks the O2 sensor(s) to see if there is a change in O2 content. If the idle period is too short the test will abort to be done later. I believe the 410 code is set when it fails to detect this change in O2 content. I think the most likely cause is the vacume supply to injection valve. Check the vacume lines and elbows from the solonoid valve on left fender to the injection valve on the exhaust side. Also check the vacume supply to the solonoid valve. You can also check for presence of vacume at the valve by pulling off the vacume line during the time the air pump is running after start up. All the above assumes the air pump is starting up OK and I think it is otherwise there would be a different code.
I am not sure if CEL comes on as soon as the initial fault is detected. It may take several reoccuring failures before it decides something is wrong.
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David Hunter