Here is link to the 2012 GM VIN Decode
It looks like places 4 and 5 describe the car type and transmission. FS = Camaro SS Manual. So looking at the list FJ = Camaro SS Automatic.
You can chack out the pdf.
2012 ZL1 - #413 - IOM - Mods; Exhaust Commander. GMG Third Brake Light Pulsar, Tinted Windows, color matched Engine cover, ZL1 Floor Mats