You have 2 ids with the same name and the form gets broken, always provide different ids on a page:
<form method='post' id='back_button_form' action=''>
<p class="form-submit">
<input name="back_button_img" type="image" id='back_button_img' src="https://wordpress.stackexchange.com/questions/345310/back.png"/>
</p>
</form>