I want the user to be notified if they enter an incomplete mailing address.
Because mailing addresses exist in a wide variety of formats, there is no standard way of validating them. You can use REGEX expressions to validate postal codes, credit card numbers, and other inputs that follow a standard pattern (https://help.surveygizmo.com/help/textbox-answer-formats#regex-patterns-for-complex-validation). But there are no off-the-shelf expressions that will validate mailing addresses.
There are online utilities that will help you build your own REGEX expression. There is a link to one (RegEx Tester) in the SurveyGizmo documentation. This is probably your only option.