My 2004 f150 truck parking light are flashing and wont turn off

interesting. could be light switch, or a relay/ relay timer or setting:
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https://www.google.com/search?source=hp&ei=oQQEXbeoAYim_Qb05bOoBQ&q=2012+ford+f150+parking+lights+wont+turn+off&oq=2012+Ford+F150+%5Barking+light&gs_l=psy-ab.1.1.33i22i10i29i30l8.1824.11879..15649...5.0..0.335.3360.4j12j3j2......0....2j1..gws-wiz.....0..0j0i10j0i22i30j33i22i29i30j33i160j0i13j0i13i30.pljyQJU6YZM
2.

https://www.google.com/search?source=hp&ei=oQQEXbeoAYim_Qb05bOoBQ&q=2012+ford+f150+parking+lights+wont+turn+off&oq=2012+Ford+F150+%5Barking+light&gs_l=psy-ab.1.1.33i22i10i29i30l8.1824.11879..15649...5.0..0.335.3360.4j12j3j2......0....2j1..gws-wiz....

3.
trailer light fuse(wetness):
https://www.fordf150.net/forums/viewtopic.php?t=27908
4.

http://www.fixya.com/cars/t3976577-parking_lights_stay_after_truck_off

Some speed wheel sensor got o bad or need adjust.

I would check your battery. I would also look for loose grounds. The clicking you hear is your fuel pump turning on. I would check your battery voltage and, have the battery load tested.

Check the park aid sensor lenses for damage.

Next remove the park aid sensors ( remove from the back of the bumper ) and check for damage.

Check the connectors on the sensors for corrosion or damage.

The symptom you describe is usually the park aid module cannot test the sensors ( or they fail test )

I have a 2004 f150 xlt triton. I couldn't figure out the how to turn on the fog lamps and the manual was not helpful.

Solution: turn the light switch all the way to the right and pull the switch (out) towards you. Push switch in and it turns off. The manual says to turn switch all the way to right but doesn't say to pull switch out.

There is another recall on the cruise control. The first added a fuse. This new recall is about wiring and lighting problems caused by the cruise. Everything from not shifting out of Park to no brake lights to false dash indicators. Best to contact the dealer, if it is a recall its free.

Is the light flashing fast when you turn the key?? If it is then the key became deprogrammed and you will have to use the other key. If there is no other key then it will have to go to the dealer or a mechanic with a computer that can access the vehicle computer to reprogram the key

probaly the parking brake not fully released or the cable is sticking.
Parking brake is wired to the brake light too.

This is the problem with faulty reverse light switch which is in the transmission, replace the switch it will the problem ...

Good luck....

If the trans won't go out of part then the part lock-out is engaged, this is disengaged when the brake lights are activated, make sure the brake lights work, if they don't check the brake light switch (and the fuse) with a 12 volt test light to see if it works, until they work u are stuck.