When will the green TAD OFF annunciator illuminate?

The illumination of the green TAD OFF annunciator indicates that the TRIM AID switch is set to off. This is a key feature of the TAD (Trimmable Aircraft Design) system, which assists in stabilizing the aircraft during flight. When the switch is disengaged, the system stops providing this stabilization, signaling to the pilot that they must manage the aircraft's trim manually.

In the context of the other choices, while the TAD system's failure or the aircraft being on the ground might affect various indications in the cockpit, they do not specifically trigger the TAD OFF annunciator to illuminate. Likewise, the state of the engine being off is unrelated to the status of the TRIM AID switch. Therefore, understanding the function of the TAD system and its associated indicators is essential for proper interpretation and response during flight operations.