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Since this is new vehicle to you the first thing I would do is check for an aftermarket remote starter. You might be able to tell by popping the hood and looking for an installed pin switch or a sticker that warns a starter is installed. If you can contact the previous owner and ask them that is another option. You could also look up under the dash on the driver side for a black box with a bunch of wires and some relays. Typically there will be plastic tie wraps holding everything in place and it will look like the wires are running to the ignition switch, the brake pedal switch and the light switch.
I have seen many of these aftermarket starters malfunction and this is just one symptom! Sometimes you will have random flashing lights or mystery clicking sounds, etc...
That is probably the remote starter, can you see any words on it? It's possible you could just unplug it and that would disable the remote starter. The easiest way to test it is to unplug it and make sure the vehicle starts and everything still works.
I doubt the module would cause this. It's possible someone has changed the code from the factory code. A Ford dealer can put their scan tool on it and check the entry code.
The box you are seeing might be a factory box. Do you see a part# XXXXX anything else stamped into it?
The crimestopper box is the main control unit. You should be able to unplug this and completely disable the remote starting. If you are uncomfortable doing this I would suggest taking it to someone you trust and ask them to remove the aftermarket modules from the vehicle.