Buy a 167A Denso (135A Denso's started coming on the Mustangs in 2010) from me for $325 w/ no core charge and you will never have an issue again.
And run 2ga to the alternator.
The 6G alternator design (the stock one) is a flawed design. No matter who makes it/re-builds it/hot rods it they have problems, lots of problems. They're junk.
The oem 135A alternator in the 2010+ cars is a 3 phase unit. The 05-09 cars got the single phase unit. If the 167A denso is a 3 phase unit as well.... it will be a winner.
Baffles me why Ford would use a single phase alternator in the 05-09 cars. I was sure that single phase alternator's had gone the way of the do-do bird a looong time ago. At least with other car maker's.