I need a sweet communicator I can give my alligator to

So I just listened to the "Fab 4 Free For All" (which if you don't listen to, you really should start!) review of the latest Paul McCartney album, "New."   Wow....I really had no idea what the song "alligator" was about!    I am a bit clueless at times I guess.    Here I thought Paul was talking about going to the zoo with his daughter or something along those lines....and really Paul was being a naughty boy!