Hey there Bluewhistle,
We understand you're having issues with the Mail app signature feature. It either is not available in the drop-down menu or doesn't appear automatically. We'll be happy to help.
To begin, we'd recommend double-checking the steps you're using to create and select the signature using the steps here: Create and use email signatures in Mail on Mac
Make sure to notate the section about automatically adding them to emails.
If the issue persists, try adjusting your signature to something else. It's possible it may be related to formatting. Generally, a less complex signature will be good for testing.
And if it still occurs, we could create a new user account on your Mac to help us determine if there is something on the account causing issues. To create the new user, check out the steps here: Set up users, guests, and groups on Mac
Let us know how that goes. Cheers!