I am trying to validate the billing email and phone number inputs on this page using a script that is already in place on the site:

Test Page

I have tried all sorts of variations, and can't get it to work. Clicking submit with the email and phone fields empty triggers the "email required" message as intended. However, putting an email address into the field doesn't stop the message from appearing, and the form won't submit. Can anyone see what I'm doing wrong?