According to my dad, who owns a John Deere, the VIN (Vehicle Identification Number) on John Deere machines tend to be located on the lower left corner of the frame, around the back of the tractor. I'm not sure if the same applies to Gators, but it's worth giving it a try!
What If It's Not There?
Try looking around the engine. The number you're looking for should be six digits long, apparently - don't quote me on this, as it's only what I've heard!
And If I Still Can't Find It?
Your best bet is probably to call up your nearest John Deere dealer - even if they just deal in parts rather than whole Gators - and they'll be able to help you find what you're looking for.
Sorry I couldn't be of more help, and good luck finding that VIN!
