what we need is a diagnostic scan using a ford scanner or equivalent to read the antitheft module and retrieve the fault codes
1-it could be a number of things that is making the alarm go off , from the key lost sync with module, door micro switch that tells system if open or close , hood switch , trunk, antenna receiver , anti theft module itself etc...
2- make sure that battery has 12 volts and you are charging 14 volts with all load on while running , like ac ,headlight ,flasher etc.. low voltage will trigger it
you can try resetting it using the procedure below , but that want solve it permanently , if it will reset at all, if it is a hard fault , it want reset .
Master reset Procedure
1- Disconnect Battery Cables ( Negative & Positive Cables )
2- Hold cables Together for 60 secs ,then let go
3- Wait 15 minutes
4- Make sure all doors are closed
5- Reconnect battery Cables
6- Lock & unlock the vehicles using the key from driver door side (if you have a key fob with no blade key, just lock & unlock using the key fob buttons)
7- Enter the vehicle and attempt to start
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