The P0410 is an indication the pump is not running when commanded to. Is the pump running, say, at cold start up like it's supposed to?

What blue and black module did you replace? What do vacuum hoses have to do with that pump?
(Honestly asking here, because I really thought that this system was simple - it takes air and pumps it into the exhaust at start up to help the converters to heat up and do their job better. I kinda don't think vacuum lines have anything to do with it, but don't know for sure.)