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It's a lot more difficult to modify wiring on a newer car like yours than the old 60's rides most of us around here work on. Lots more going on. A quick Google search yielded a number of wiring diagrams detailing 2010 mustangs. From what I found looks like fuse #22 is the lighter. Not sure what good that will do you though, honestly. You need to identify a keyed power source and tap the lighter lead into that but unlike older cars I don't see any place that is just a basic source to tap into. If you could find a full wiring diagram I could direct you on exactly what to do.
A simpler way to get it done would be to use the power lead to the radio to power a relay coil to control a contact that would make/break the original power wire leading to the lighter. That way the factory fuse circuit is still in place. The draw of the relay coil would not affect the radio circuit fusing at all. Just splice into the 12+ power wire of the radio to the coil + and run the coil negative to a metal ground under the dash. Cut the existing lighter power wire and put one end on one side of the relay open contact and the other to the other side of the same contact. The relay will energize and close when the key is in ACC or on and close the contact power the lighter socket as you want.