Yes, PoppaGater, I do too.
My grandmother was a Healer-type lady - although she didn't carry an aligator purse. There was no symbol of her trade that I recall or see in any of her photos. (Of course she was Australian). She was often called after the doctor and the nurse had given up on someone.
I reckon that it's just as likely as not that a symbol that turns up in a song has some significance. It's finding the connections from outside the song that may help us.
Cheers, Joy