My 2002 is doing the exact same thing. My battery is about a year old and I just replaced alternator. Mine is still doing it. Makes lights go a little dim and then comes back to normal. Very intermittent. Doesn't do it all the time. This seems like an alternator problem, so not sure if the new one I got is a bad one but my meter is reading like it's ok. So not sure. I think is a common mustang issue with these years.