How to reuse object between Drupal Behaviors?
I'll focus on the inclusion first, then describe what Clive was referring to, while mentioning that your JS is not valid:

For your use case you should add a common library to your module/theme that extends the Drupal object. (You don't even have to extend the Drupal object, but can create an own one, if you prefer.)

Then use dependencies to make sure the object is available in your basic page JS, as well as in your article JS.

Example

In your *.libraries.yml

mymodule/common:
  js:
    js/mymodule-common.js: {}
  dependencies:
    - core/drupal
    - core/jquery

mymodule/page:
  js:
    js/mymodule-page.js: {}
  dependencies:
    - mymodule/common
    - core/drupal
    - core/jquery
    - core/jquery.once

mymodule/article:
  js:
    js/mymodule-article.js: {}
  dependencies:
    - mymodule/common
    - core/drupal
    - core/jquery
    - core/jquery.once


You can then split your JS to the three separate files containing your code. The dependencies section makes sure the scripts your library depends on are loaded before.

Now to the scripts itself:

mymodule-common.js

(function($) {
  'use strict';

  Drupal.customObj = {
    'function1': function(element) {
      /* perform some logic here */
    },
    'function2': function(var) {
      /* perform some other logic here */
    }
  };

})(jQuery);


mymodule-page.js

(function($) {
  'use strict';

  Drupal.behaviors.customName = {
    attach: function(context, setting) {
      $('body').once('customName').each(function() {
        var func1 = Drupal.customObj;
        var results = func1.function1($('body'));
        //process results
      });
    }
  };

})(jQuery);


And similar in your mymodule-article.js.

And here the promised feedback to the comment of Clive: Compare the attach property in the last example. It expects a callable that will be executed every time a page/ajax load finished. Within its body you can then do your magic.

References:

https://www.drupal.org/docs/8/api/javascript-api/javascript-api-overview
https://www.drupal.org/docs/8/theming-drupal-8/adding-stylesheets-css-and-javascript-js-to-a-drupal-8-theme