What component is likely at fault if pilot gas continues to flow after the pilot has been out for a few minutes?

When pilot gas continues to flow after the pilot has extinguished, it indicates a potential failure in the safety mechanism designed to shut off the gas supply. The safety valve is responsible for controlling gas flow based on the presence of a functioning pilot flame. If the pilot goes out, the thermocouple, which generates a small voltage when heated, should signal the safety valve to close and stop the gas flow to prevent hazardous situations.

In this case, the safety valve not closing after the pilot has gone out suggests it may be faulty or malfunctioning, allowing gas to leak despite the absence of a flame. Thus, the continued flow of pilot gas points directly to a problem with the safety valve, confirming it as the correct answer.