X358 secondair air injection codes solved

Short story: codes 0411 and 0414 on an ‘06 VDP were traced by the dealer to a faulty solenoid in the secondary injection system. Took two visits. First time codes had cleared themselves, but dealer replaced the brittle vacuum hoses, a cracked air hose downstream of the MAF and what i think was called a diverted valve toward off future problems. $700. Reappearance of codes a few weeks later led to the solenoid. Part was $25. Labor to diagnose (over 3 days) another $200 or so. Nice part —a rental to use gratis in the interim. If the CEL comes on again I’ll be dismayed.