This sounds like your SJB(smart junction box) is the problem. It's a higher tech BCM/GEM and handles all secondary electrical systems and even primary systems like PATS and PCM to cluster communication. There are common water intrusion issues with the 2005-09 Mustang that can lead to water on/in the SJB. There's a TSB that Ford released that describes these areas and the fixes for them: tsb08-26-07.pdf (mygtcs.com). The 2005-14 Mustangs all have a tendency to have the cowls clog up with leaves/debris and then overflow thru the fresh air vent into the HVAC system in the passenger compartment and then onto the SJB.
If the SJB has ever gotten wet then it can cause corrosion and/or a malfunction that may require repair or in worst cases replacement. If it turns the SJB is the problem then you can have it sent out to a module repair service. Automotive Circuit Solutions, Autoecm, Upfix, and Module Master all seem to be reliable module repair services to use. They can test and if needed repair any module as long as damage isn't too severe. Getting a brand new SJB is not an option and a used one is a gamble to which you would have to buy the same part # as what you have in the car based off of the available factory options. It's best to just remove your SJB and send it out to one of those companies to have them test it.
If the SJB has ever gotten wet then it can cause corrosion and/or a malfunction that may require repair or in worst cases replacement. If it turns the SJB is the problem then you can have it sent out to a module repair service. Automotive Circuit Solutions, Autoecm, Upfix, and Module Master all seem to be reliable module repair services to use. They can test and if needed repair any module as long as damage isn't too severe. Getting a brand new SJB is not an option and a used one is a gamble to which you would have to buy the same part # as what you have in the car based off of the available factory options. It's best to just remove your SJB and send it out to one of those companies to have them test it.