The song is about Coronel Tom Parker, manager of Elvis Prestley. Coronel was a semi-legal immigrant, almost a con-man, working in side shows. Then he met Elvis-"a country boy, a bird who sings", and reportedly made him (actually his parents) sign a horrendous contract. It practically put Elvis in complete dependence, while Tom got most of the money. Comparrison to a gator means that when the coronel got a hold of you, he won't let you go. Pretty much what he did to his most famous client.