[Mr 5 0]

You have a 15-year-old Mustang and even with low mileage some things just go bad from age, rot, corrosion, etc. This may be one of those instances.

Assuming your battery is fresh and not compromised or undersized, you might want to try investing in new battery cables (negative and positive) as well as checking your ground for a bad connection. I would also replace the TFI module, which I suspect may be the real culprit.