2007 Mercury Milan 4-Cylinder P2258 Code: Check Engine Light, Rough Idle, and Secondary Air Injection System Diagnosis

Hi there! I'm currently dealing with a 2007 Mercury Milan with a 4-cylinder engine that has the check engine light illuminated. After using a code reader yesterday, I retrieved fault code P2258, which is related to the secondary air injection system. The car exhibits a rough idle at startup and inconsistent RPMs when the throttle is applied. Based on my research, P2258 typically points to issues within the secondary air injection system — potentially involving the solenoid, the air pump, or even the Powertrain Control Module (PCM). Ford service technicians often replace entire components in this system if they detect this code, which can cost between $1,000 and $2,000. As a beginner with car diagnostics, I'm looking for practical troubleshooting steps to identify the root cause without overspending. Can anyone recommend where to start? Any advice on testing specific parts or diagnosing the issue step-by-step would be greatly appreciated.