The Solution
In case you are interested, the key to getting the HMTL script to pass SELECT data is to 1) declare your variable as an array, i.e. use brackets like product[], 2) Then in your PHP action script make sure you treat product as an associative array, i.e. forech($_POST['product'] as $key=>$value). Note, this allows you to pass over multiple selections.
Also, note the use of _POST. If you are still using PHP4 it is important to look at _SERVER, _GET, etc. because you will undoubtly cross their path during forms development. You can use the long names like HTTP_POST_VARS but the shorter names are more managable.