Door ajar alarm

Your best bet would be to find a Tech like this guy , with the right diagnostic equiment . Door Locks Go Crazy 1 Unless you know how to do automotive electrical testing . Your door ajar switch is a input to a body control module . or GEM as ford calls thiers .
Door Locks Go Crazy 2 Your auto lights are controlled pretty much the same .
Electric Testing Techniques You Need to Know

Do you know what DTC"S are ? diagnostic trouble codes ! You probably have a door ajar switch problem . You need a factory or professional type scan tool to check these codes
B1322 Door Ajar Driver Circuit Short to Ground GEM/CTM REFER to Section 417-02 . B1323 Door Ajar Lamp Circuit Failure GEM/CTM REFER to Section 413-01 . B1325 Door Ajar Lamp Circuit Short to Battery GEM/CTM REFER to Section 413-01 . B1330 Door Ajar RF Circuit Short to Ground GEM/CTM REFER to Section 417-02 . B1334 Decklid Ajar Rear Door Circuit Short to Ground GEM/CTM REFER to Section 417-02 . B1338 RR Door Ajar Circuit Short to Ground GEM/CTM REFER to Section 417-02 . B1340 Chime Input Request Circuit Short to Ground GEM/CTM GO to Pinpoint Test C .

• The Autolamps Are On Continuously

• Circuitry.
• Headlamp relay.
• Light sensor amplifier.

• Go To Pinpoint Test H .

• The Autolamp Time Delay Is Inoperative

• Fuse(s).
• Light sensor amplifier.
• Headlamp switch.
• Circuitry.

• VERIFY parking lamp operation. If OK, REPLACE the light sensor amplifier. If any parking lamp concerns exist, Parking, Rear and License Lamps REFER to Parking, Rear or License Lamps.

Do you see how complex these systems can be for someone that doesn't deal with these problems on a daily base's ! Check for codes an if there are any , doing the diagnostic's associated with it . Without doing the diagnostic's you could replace parts all day long an not fix the problem .
2002 2005 Ford Explorer Door Ajar Light Common Door Wiring Faults

Rusty or loose connection on one of the door switches...

contact ford manufacturer custom relations department and make noises about it as there may be a service fix that was not done for you under warranty by the dealer.

Subject; 2006 Ford Escape

Re: dome light, door ajar lamp on dash, uncontrollable alarm activation. I just purchased the subject vehicle and did have problems with the factory (OEM ) alarm going off through the day and night. The first thing I did to fix the problem was; I removed all the door locks from each of the doors and disassembled them to ensure proper operation of the micro switches within each of the door locks. I also checked the hood trigger switch to ensure it was functioning correctly. I removed the plastic cover on the inside of the hatch to ensure proper function of the two door latches under it (one for the hatch the other for the glass). Still having the problems I originally had I decided my problem could be a bad ground to the frame. So I made another ground from a trigger switch to the chassis (frame). I made my ground connection above the headliner on the right rear of the vehicle. Raise the main rear hatch and pull the top section of the plastic corner post panel back, pull the headliner down to expose the multi pin connector going to the rear hatch wiring. In that bundle of wires is a black/White stripe wire. I soldered a wire to that wire and attached the other to ground. I would not suggest removing the locks from your doors or hatch, and oil/WD-40 won't work either. However high pressure air with carburetor cleaner seem to work best for me in making the door locks work smoother. Basically all the cleaner does is removed dirt and dust buildup from around the micro switch assembly within each door. You could potentially have a bad door lock to but can isolate them one by one. Good luck.

Try spraying wd40 into each door latch. Do it one at a time then open and close the door about a dozen times spray some more in there after about 6 open and closes. Do this with each door and even the hatch. This should clear ya right up.

do you have any of the warning lights on in the dash??? maybe a door ajar or the rear hatch or hatch window

This is probably caused by:

a loose door switch, or

a loose connection to a door switch, or

a defective (dirty / corroded) door switch.

There is a false signal being sent that a door is open / ajar.

The liftgate consists of the following components:

• liftgate door lock actuator
• liftgate lock cylinder (if equipped)
• liftgate window glass
• liftgate window latch/ajar switch
• liftgate window glass release handle
• liftgate latch remote control which consists of the following component:
  • liftgate release handle
• liftgate latch, which consist of the following component:
  • liftgate latch door ajar switch

Liftgate Latch Actuator Removal and Installation

1. Remove the liftgate latch remote control. For additional information, refer to Liftgate Latch Remote Control in this section.

SECTION 501-14: Handles, Locks, Latches and Entry Systems 2001 Escape Workshop Manual
REMOVAL AND INSTALLATION Liftgate Latch Removal and Installation

1. Remove the liftgate trim panel.

1. Disconnect the liftgate ajar switch electrical connector.

1. Disconnect the liftgate latch actuating rod.
   1. Open the clip.
   1. Disconnect the actuating rod.

1. Remove and discard the liftgate latch bolts.

1. Remove the liftgate latch.

1. NOTE: Make sure the liftgate latch release rod is not preloading the latch. It should be clipped in a relaxed state with no slack.
   NOTE: Position the liftgate latch release rod by pushing outboard to remove the slack.
   

1. Remove the screws and the liftgate latch actuator

there is a switch in each door that senses the door is open, it is called the door ajar/courtesy light switch (imagine that), they stick and have this problem, replace it.

What happens when you remove both switches, and wires? What happens when you use a jumper wire acros both wires, on both doors?