How much do you want to bet that the air pump is working?
Why would you get an "air pump does not work" for only one bank? Clogged ports maybe, but other than that, you wouldn't.
Many have had these codes (myself included) and it's almost always a bad changeover valve or a vacuum leak. I'm going by real world experience and don't care what some incorrect book says.
Either way, you use logic: these codes are triggered by incorrect voltage at the pre-cat O2 sensors (0410=bank one, 1411=bank 2), meaning that there is insufficient airflow at the indicated bank(s) during SAI cycle.