I have a form in which the Submit button does not sit within the tags. The submit button has an click handler to submit the form via jQuer
This seems to be an old question, but since I just ran into a similar issue and found a good solution (for me), I thought I'd post it:
$('#admin_form').trigger('submit', [ { 'variable_name': true } ]);
or
$('#admin_form').trigger('submit', [ 'variable_name', 'true' ]);
depending on whether you want to pass a variable called variable_name with value true or you want to pass 2 separate variables.
And just to be clear, this will not of course automatically submit variable_name with the rest of the form fields, but if you have a submit handler, as I do in jQuery, the variables will be passed as arguments, after the event.