custom checkout pane submission
The short answer is you can't do what you want, but there are other things you can do. You need to look into using the #ajax properties of form elements to submit data to the server when the customer clicks your button without initiating a POST redirect as you would for a full form submission.

However, that will still trigger a validation of the entire form, not just the pieces that you specifically want to validate. What Drupal allows you to do is limit validation errors from resulting in form errors when the form is rebuilt.

The topic is honestly a big bigger than can be answered here, but I hope this points you in the right direction. The best thing to do will be to investigate how a module with similar functionality achieves what it is you want to do and imitate the code (if it's up to date and / or well-maintained ; ).