Why did she ask for the walking stick? Well, usually, the staff was where you placed your signet and your cord. You hung the signet from the cord that you placed on your staff. So, all three kind of go together. All three of them, then, would identify Judah. Not just any one, but all three of them would really say, "You're the man."
I do need to explain something. It says there, in verse 15, that Judah thought that she was a harlot. That word is the normal word for prostitute, for harlot. But when you get down to verse 21, the word that Hirah the Adullamite uses is not "harlot." It's "ritual prostitute"—a different word. (Qedeshah.) It means "holy prostitute" or "set apart prostitute."
She did was not pose as a mere prostitute. She posed as a priestess of Ashtoreth and part of the ritual of that religion was that a woman could become a ritual prostitute in Ashtoreth's temple, as part of her service to the goddess.
