How to programmatically trigger a click on an AJAX enabled form submit button?

jQuery('#edit-submit').mousedown() - apparently there's a big difference.

Actually, there's no need to guess.

You should use Drupal behaviors

Drupal.behaviors.yourFunctionName = {
    attach:function (context, settings) {

       // Your code goes here....

    }
}

This will give you access to the settings' ajax property,

Drupal.behaviors.yourFunctionName = {
    attach:function (context, settings) {

       console.log(settings.ajax);

    }
}

Depending on your configuration, you should see a list of triggering elements, with various properties such as the name of the callback function, the selector's id as well as the name of the triggering event.

You can then use the relevant information to trigger your event.

// $(selector).trigger(eventName);
// for example...
$('#edit-product-id-15', context ).trigger('change');

Create ajax submit like the following.

 $form['button'] = array(
    '#type' => 'button',
    '#value' => 'Click',
    '#ajax' => array(
      'callback' => '_kf_reading_user_points',
      'wrapper' => 'reading-user-points',
      'method' => 'replace',
      'event' => 'click',
    ),
  );

function _kf_reading_user_points(&$form, &$form_state) {
  // Something within the callback function.
}

Then the jquery .click() event would be work in the drupal ajax form.

You can also use .trigger() jQuery method. $('#element').trigger('click');

In my case, the above recommended solutions didn't work for me, but the mention of .mousedown() led to the following idea that worked for me (Drupal 7):

$('#custom-submit-button').click(function() {
  $('#ajax-submit-button').trigger('mousedown');
});

There's some helpful background info about "why" this is the case in the Form API Reference under #ajax_prevent

Looking at the Better Exposed Filters module, they submit the AJAX form by finding $(.ctools-auto-submit-click') and trigging a click.

<?php
// ... near line 190 of better_exposed_filters.js

// Click the auto submit button.
$(this).parents('form').find('.ctools-auto-submit-click').click();
?>

You have to trigger the submit event on the form. Click and mousedown events on buttons are not working.