Intro
This article can also be found HERE as a part of my blog.
How jQuery Mobile handles page changes
To understand this situation you need to understand how jQuery Mobile works. It uses ajax to load other pages.
First page is loaded normally. Its HEAD and BODY is loaded into the DOM, and they are there to await other content. When second page is loaded, only its BODY content is loaded into the DOM. To be more precise, even BODY is not fully loaded. Only first div with an attribute data-role="page" will be loaded, everything else is going to be discarded. Even if you have more pages inside a BODY only first one is going to be loaded. This rule only applies to subsequent pages, if you have more pages in an initial HTML all of them will be loaded.
That's why your button is show successfully but click event is not working. Same click event whose parent HEAD was disregarded during the page transition.
Here's an official documentation: http://jquerymobile.com/demos/1.2.0/docs/pages/page-links.html
Unfortunately you are not going to find this described in their documentation. Ether they think this is a common knowledge or they forgot to describe this like my other topics. (jQuery Mobile documentation is big but lacking many things).
Solution 1
In your second page, and every other page, move your SCRIPT tag into the BODY content, like this:
<body>
<div data-role="page">
// And rest of your HTML content
<script>
// Your javascript will go here
</script>
</div>
</body>
This is a quick solution but still an ugly one.
Working example can be found in my other answer here: Pageshow not triggered after changepage
Another working example: Page loaded differently with jQuery-mobile transition
Solution 2
Move all of your javascript into the original first HTML. Collect everything and put it inside a single js file, into a HEAD. Initialize it after jQuery Mobile has been loaded.
<head>
<meta name="viewport" content="width=device-width; initial-scale=1.0; maximum-scale=1.0; minimum-scale=1.0; user-scalable=no; target-densityDpi=device-dpi"/>
<link rel="stylesheet" href="http://code.jquery.com/mobile/1.2.0/jquery.mobile-1.2.0.min.css" />
<script src="http://code.jquery.com/mobile/1.2.0/jquery.mobile-1.2.0.min.js"></script>
<script src="index.js"></script> // Put your code into a new file
</head>
In the end I will describe why this is a part of a good solution.
Solution 3
Use rel="external" in your buttons and every elements you are using to change page. Because of it ajax is not going to be used for page loading and your jQuery Mobile app will behave like a normal web application. Unfortunately this is not a good solution in your case. Phonegap should never work as a normal web app.
<a href="#second" class="ui-btn-right" rel="external">Next</a>
Official documentation, look for a chapter: Linking without Ajax
Realistic solution
Realistic solution would use Solution 2. But unlike solution 2, I would use that same index.js file and initialize it inside a HEAD of every possible other page.
Now you can ask me WHY?
Phonegap like jQuery Mobile is buggy, and sooner or later there's going to be an error and your app will fail (including loaded DOM) if your every js content is inside a single HTML file. DOM could be erased and Phonegap will refresh your current page. If that page don't have javascript that it will not work until it is restarted.
Final words
This problem can be easily fixed with a good page architecture. If anyone is interested I have wrote an ARTICLE about good jQuery Mobile page architecture. In a nut shell I am discussing that knowledge of how jQuery Mobile works is the most important thing you need to know before you can successfully create you first app.
