2005 lincoln aviator. motor runs rough at idle

Various types of help here

https://www.google.com/search?q=2005+Lincoln+Aviator+GEM+module+location

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Question edited for clarity.
Question moved to the correct vehicle category..

Your air ride suspension has failed..

https://www.google.com/search?q=2005+lincoln+aviator+air+suspension

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Could be EGR dirty or stuck; tune up items; IAC dirty or failing; vacuum leak.

This has a double intake manifold with control actuators at the base of the manifold most are vacuum controlled the computer monitors these actuators positions. #1 locate passenger actuator and lever position with engine off put a vacuum hose on it and suck on hose and watch arm lever it should move then place tongue against hose it should hold that position if it does not actuator is bad if it does the the control solenoid is at fault or no engine vacuum to solenoid.

Duplicate question

On the Lincoln Aviator there's a set of fuses under the dash of the vehicle. One set has to be dropped to get to the flasher fuse.

What codes did you get from the check
light being on. Have to start there

The COPS (coils) may have shorted the drivers in the PCM (computer). You should get a misfire code for each cylinder misfiring though.

Slim possibility, but very expensive unless you have a service contract.
LINCOLN: 1999-2004 Navigator
2002-2003 Blackwood
2003-2005 Aviator MERCURY: 2003-2004 Marauder
ISSUE: Some 1999-2004 Navigator, 2002-2003 Blackwood, 2003-2005 Aviator, 2003-2004 Marauder and 2003-2004 Mustang vehicles built before 12/19/2004 equipped with 4.6L 4V/5.4 4V engine may exhibit a runs rough, lacks power, and engine misfire, prompted by a MIL light and DTC codes P0301, P0302, P0303, P0304, P0305, P0306, P0307, P0308, and P0316.
ACTION: Diagnose engine for engine misfire concern. If diagnostics determine an engine misfire which is characterized by leakage through exhaust valve(s), only replace the affected cylinder head(s).
SERVICE PROCEDURE FOR VEHICLES WITH RUNS ROUGH/MISFIRE CONDITION:

1. Perform relative compression check on all cylinders. If abnormal, check cylinder leakage and actual compression for "low" cylinders refer to Workshop Manual (WSM), Section 303-00.
2. If leakage/compression check indicates a valve train concern, per valve train diagnostics in WSM, Section 303-00, replace cylinder head and cam assembly, pipe plugs and timing chain tensioner, per procedure outlined in WSM, Section 303-01.
3. If cylinder leakage and compression tests are inconclusive, perform misfire diagnostic, per TSB 05-22-8. NOTE: DO NOT TRANSFER SPARK PLUGS. INSTALL NEW SPARK PLUGS IN REPLACEMENT CYLINDER HEAD AND CAM ASSEMBLY. NOTE: THE ENGINE MISFIRE CONCERN IS TYPICALLY EXHIBITED ON THE LEFT HAND CYLINDER HEAD AND RARELY ON THE RIGHT HAND CYLINDER HEAD. UNLESS CONFIRMED, THE RIGHT HAND CYLINDER HEAD SHOULD NOT BE REPLACED AS AN "EXTRA MEASURE" SERVICE PRECAUTION. NOTE: THE REPLACEMENT CYLINDER HEAD WILL NOT IMPROVE OR REDUCE ENGINE HORSEPOWER OR TORQUE ABOVE ADVERTISED LEVELS.
   

Hi! As a first course of action please check the sparkplugs. If the plugs are full of carbon this can cause a rough idle on the car. You will need to clean or replace the plugs if necessary. Hope this helps and thank you for using FixYa!

If there is an Auto Zone around your area, have the truck scanned for the DTC codes which is causing your idle problem. There are to many things that can cause your trucks idle to be rough. Once you have it scanned, we can address the issue and have your truck running 100% again. Auto Zone scan free of charge and can give you the step by step instructions to repairing and replacing the parts needed. Good luck and keep me posted, be glad to help.