The malfunction indicator light must illuminate when:

The malfunction indicator light, commonly known as the check engine light, is designed to provide essential information about the vehicle's engine and emissions systems. When the ignition key is turned to the "on" position without starting the engine, it should illuminate as part of the self-check diagnostic process that occurs when the vehicle is powered on. This ensures that the driver is aware that the light is functioning properly and will illuminate if there is a malfunction after the engine is started.

This function is critical for vehicle safety and maintenance, as it alerts the driver to potential issues that may arise. If the light does not turn on in this scenario, it could indicate a malfunction in the light itself, which may lead to missed warnings about important engine or emissions system issues.

The other scenarios presented do not serve the same diagnostic purpose. For example, having the vehicle in motion or parked with the doors locked does not allow for the comprehensive system checks that occur when turning the ignition to the "on" position. Additionally, when the engine is running at idle, the light should normally be off if all systems are functioning properly, as constant illumination while the engine runs could indicate an active problem rather than a self-diagnostic check.