P2631 Lincoln the main thing to check is to verify the operation of the VCT solenoid. You're looking for a sticking or stuck VCt solenoid valve caused by contamination. Refer to vehicle specific repair manual to perform component tests for the VCT unit.
Accelerator Pedal Position Sensor 1 Circuit Low and P2127 - Accelerator Pedal Position Sensor 2 Circuit Low would lead you to suspect a defective accelerator pedal position sensor.
Indicator and headlight bulbs need regular maintenance for them to keep functioning properly. Also the car paint ought to be in good condition because that reduces the chances of rust taking over the body of your car. This is one of those car maintenance problems, which are easy to handle, given the variety and quality of products available in the market today.
P2631 meaning and repair processes are the same for all Lincoln models.
P2631 Lincoln Trouble Repair Process:
If your vehicle failed a P2631 Lincoln test and the P2631 Lincoln Check Engine Light is NOT on, chances are you have a problem with the OBDII system, a burned out MIL lamp, or a faulty catalytic converter. The converter is essentially an afterburner that cleans up the exhaust after it exits the engine. The OBDII system uses a ownstream oxygen sensor to monitor the efficiency of the converter, and it should detect a drop in converter efficiency if the converter has been contaminated or is failing (ignition misfiring, leaky exhaust valves, and oil burning can all damage the converter). What you want to look any conditions that might cause ignition misfire, an overly rich or lean fuel condition, or loss of compression. Use your OBD Express DIY to look at the oxygen sensor outputs, coolant temperature, airflow, calculated engine load, and inlet air temperature.
p2631 is a very common fault code for the thermostat. If you have this fault it will need to be replaced. I would start with that repair, clear the faults and perform a 30 minute battery reset(disconnect the negative cable off of the battery) and retest the vehicle.