To determine which sign indicates a faulty starter solenoid, we must first understand the function of a starter solenoid in an engine and the symptoms of its failure:

Function of a Starter Solenoid: The starter solenoid is a crucial component in an automotive ignition system. It is responsible for transmitting electrical current from the battery to the starter motor when the ignition key is turned. This action is what enables the engine to crank and ultimately start.

Key Symptoms of a Faulty Starter Solenoid:

1. Clicking sound but engine does not turn over: This is a classic sign of a faulty solenoid. When the solenoid fails, it might not engage the starter motor properly, leading to a clicking sound without the engine turning over.
2. Engine cranks faster than normal: This typically suggests inadequate compression, not a faulty solenoid.
3. Strong fuel smell during ignition: This could be indicative of a fuel leak or flooding, which is not associated with the starter solenoid.
4. Dashboard lights are brighter than normal: This is more related to the electrical system or battery issue, rather than a solenoid problem.

Conclusion: The option "Clicking sound but engine does not turn over" accurately describes a common symptom of a faulty starter solenoid. This occurs because the solenoid is unable to transfer the necessary power to activate the starter motor, despite receiving a signal from the ignition.