Can gift cards be traced back to a credit card?
Accordingly, can Amazon gift cards be traced?
No. If you can convince Amazon that someone stole your gift card, and they refund you the value that was taken, then it's no longer any of your business who stole the value.
Similarly, can you get caught using a stolen gift card?
Store security could detain them until the police arrive, and they could be prosecuted for theft and/or fraud. But if no one has yet reported it lost or stolen, it will have the full value and anyone could use it to make a purchase. That is why you should keep up with gift cards and use them as soon as possible.
Once you have the gift card number (or as much information as you can find), call customer service for the merchant that issued the gift card. The objective of the phone call is not to “find” the gift card, but to find out if the gift card has been used.