nginx / node.js sendmail form

Trying to send user feedback to email using an embedded contact form; without using a mailto:

I have a mostly static web page served up by nginx containing html/browser-javascript.

The strategy is very similar to this:

http://www.phpeasystep.com/phptu/8.html

My static page has a form section:

                            <form action="sendmail.js" method="post" id="contactForm">
                        <div class="sep">
                            <label for="name" class="txt">Name:</label>
                            <input type="text" name="name" value="" id="name">
                        </div>
                        <div class="sep">
                            <label for="email" class="txt">Email:</label>
                            <input type="text" name="email" value="" id="email">
                        </div>
                        <div class="sep">
                            <label for="tele" class="txt">Telephone:</label>
                            <input type="text" name="tele" value="" id="tele">
                        </div>
                        <div class="sep special">
                            <label for="last" class="txt">Don't fill this in:</label>
                            <input type="text" name="last" value="" id="last">
                        </div>
                        <div class="sep">
                            <label for="message" class="txt">Message:</label>
                            <textarea rows="5" name="message" id="message"></textarea>
                        </div>
                        <div class="buttonAlign submitbutton">
                        <button type="submit" class="button mediumButton" id="submit">Send Message</button>
                        </div>
                        </form>

I want the form elements passed to a server side node.js script, sendmail.js, and have that script compose an email with the form elements then dispatch.

I'm rather new to node.js and nginx and I'm not sure what I'm missing; but, its not working, the script is not running at all.

I've added nothing special to the nginx default.conf file. The node.js script is in my base directory and if I rename it, I get a file not found error. So, I know nginx is looking for it. The first line of the script file has the node.js she-bang and its chmod'ed to executable.

Appreciate any help.

I get the following message in access.log

==> access.log <==
     "POST /sendmail.js HTTP/1.1" 405 574 "https://xyzzy.net/index.html" "Mozilla/5.0 (compatible; MSIE 10.0; Windows NT 6.2; WOW64; Trident/6.0)" "-"

I'm not expecting a response to appear in the web page. I just want to execute the sendmail.js script and send an email containing the form data. Here's a 'dummy' script which attempts to create/write a 'breadcrumbs' file in /tmp

        #!/usr/local/bin/node

    var fs = require('fs');
    fs.writeFile("/tmp/test", "Hey there!", function(err) {
        if(err) {
            console.log(err);
        } else {
            console.log("The file was saved!");
        }
    });