Click on a button (that is not a button ?) with Applescript or Javascript

Okay, relative newbie here, but I have searched all the answers and tried most of the suggestions and cannot find a way to automate using Applescript or Javascript within Applescript to click a button on a specific website. I can't provide the website because it is part of a protected medical record software, but as far as I can tell the button is encoded as follows:

  <h3>Add new documents for this patient
         <!-- The fileinput-button span is used to style the file input field as button -->
        <span class="btn fileinput-button" style="float: right !important;">
            <i class="icon-plus"></i>
            <span>Add Files</span>
            <input type="file" name="files[]" multiple="">
        </span>
    </h3>

I have tried most of the Javascript (and Applescript) solutions. I have even tried the Fake app which seems to work for every other button except this one. I have searched in vain for a button id and the above code seems to be all that refers to the button. The function of the button is to bring up a Chooser window import image files.

Using tab to get to the button doesn't work because the number of tabs varies with individual patients (dynamic website ?).

I apologize in advance if this is trivial, but it is literally the last step in a long series of steps that would save me a lot of time. I figured out everything else mainly with the help on this board.

Thanks to all of you.