Shift your gaze from one eye, to the other eye, then down to the mouth, and back up.
Standard eye contact is polite, but courtship eye contact is a specific technique often called "The Triangle." Body Language Secrets: A Guide During Courtship...
If they take a sip of their drink, wait a few seconds and take a sip of yours. If they lean back, you lean back. Shift your gaze from one eye, to the