I almost have the exact same damage, only on my front bumper.
I cleaned with rubbing alcohol, and put a coat of touch up paint, followed by three, or four coats every hour, or so.
A week later I polished the gouge with a Qtip and compound. Not perfect, but not that noticeable either.
Let us know what works for you.
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2012 Base Mustang Convertible
2009 Grand Marquis