The car had 64600 miles on it and the headlights started going out while driving, which can be very dangerous. The problem is in the Light Control Module which is an expensive part (around $500 to $600 + labor).
Problems for specific Mercury Grand Marquis years:
Car problem reports
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Most reported 1999 Mercury Grand Marquis problems
The composite (plastic) intake manifold may crack near the thermostat housing and cause a coolant leak. Ford released an updated manifold that was reinforced to prevent a recurrence. No recall was issued for this problem but Ford did extend the warranty to seven years on some models from the date of purchase.
A spring in the seat belt buckle may wear or fail, causing the airbag light on the instrument panel to illuminate. Failed buckles will require replacement.
The throttle position sensor (TPS) may fail. Common symptoms of a defective TPS can be rough idle, hard starting, hesitation on acceleration, poor fuel economy, and stalling.
If you experience difficulty starting the engine when cold, stalling at idle, or hesitations during acceleration, it may be the idle air bypass valve. This valve helps the vehicle idle steady when the accelerator pedal is not pressed.