"The" script from Oakhurst Diner

Would someone please help me identify the name of typeface used for the word "The" in this Oakhurst Diner logo? Or, is it a bespoke script?

Here's another look on the diner's sign:

Thank you,


If Mark Simonson's "Coquette" had a swash italic this would be what it would look like, but as far as I know it doesn't.

- Mike Yanega