Scheduling a cron job from a function that is ran outside functions.php?

Question

I have a very simple function and hook registration in my functions.php, like this:

function do_this_thingy(){
   // I am sending myself some simple admin report mails, tested & works
}
add_action( 'mail_event_hook', 'do_this_thingy');

Then, in a page template I have a row:

wp_schedule_single_event( time() + 600, 'mail_event_hook' );
// expected: to receive message in ten minutes time. Result: no message :(

What might be going wrong?

Edit: Answers to questions:

1. Is this on a local server? No, this is a live WP site of mine.
2. How do I know that emails can be sent in the first place? The code that I use to send emails works perfectly if I simply run it from functions.php or another .php file on the server. I receive the email every time I try.
3. Am I sure the CRON job fired? I have the plugin WP Crontrol and it shows no scheduled task / cron job. I assume thus that the answer is no.
4. Are there PHP errors in the logs? I can take a look at this with debug logging enabled later today. Will update.

Answer 1

Solved, although in a pretty poor manner.

If I move the scheduler function

wp_schedule_single_event( time() + 600, 'mail_event_hook' ); 

into functions.php it starts working. Not sure why, but this is the curse of self taught developers.