When does a pilot need to cease using the privileges of their certificate following a suspension?

The correct answer is that a pilot needs to cease using the privileges of their certificate immediately upon suspension. When a pilot's certificate is suspended, it is a regulatory action taken by the FAA, and the suspension takes effect instantly. Once the decision to suspend has been made, the pilot must comply with this regulation without delay.

The other provided options do not align with the requirements governing pilot certification and suspension. For instance, waiting for appeals to be finished or notifying the FAA after ceasing flying is not permissible; the suspension is an immediate restriction. Additionally, a timeframe like 48 hours does not apply since the pilot must stop flying at the moment their certificate is suspended. This immediate cessation helps ensure safety and compliance within the aviation system.