My custom publish type section is very lengthy, so I have damaged up into 7 "steps" with buttons added via jquery that go ahead and take user to another "step" by hiding the very first section and revealing the following.

Wouldso would I trigger the publish or update button click when hitting the "next thingInch button?

I have attempted several solutions - none appear to become working.

The "step button" code:

jQuery('#button-1').live('click',function(){    
    jQuery('#acf_89').show();
    jQuery('#acf_88').hide();           
 });

To trigger a control button click event you are able to call .click()

jQuery('#button-1').live('click',function(){    
    jQuery('#acf_89').show();
    jQuery('#acf_88').hide();   
    $("#button_id").click();
 });

The issue with triggering a click the "Update" button is you will reload the page and lose your situation inside your custom walk-through wizard.

In order to save the publish quickly you will have to augment your Wordpress install with something similar to Ajax Post Save