it sounds like your rke module might be going bad, unfortunately the only true way to test is with the ford scan tool.
i had the same problem on my 94 mustang, uncommanded panic....it drove me crazy until i swapped out the module.
rke stands for remote keyless entry, it's a ford only part, but you can install it yourself.
have you tried just leaving the module unplugged, it should run fine with it unplugged as long as it is a factory ford, and not an aftermarket add on alarm.
if it is in the trunk it is most likely a factory ford module, and it should still run with it unplugged, it is just for the keyless entry.
i'm not sure if the module is interchangeable between different year mustangs.
it would also have to be in the car for the dealership to test it, theres no way to test it unless it is hooked up to the vehicle.
i hope this helps you