I can't find any reference to any of the Opengraph meta tags in item.php... can you be more specific?

You do no need to find any reference.

You simply need to add a new metatag if an image is not present.

OK. I could have just done that anyway. I wanted to to keep my code clean by just editing it where K2 sets the meta tag but it seems we don't know where that is.

I have done it the way you suggested instead and although being quite a hacky way, it does work.

It is not hacky.
You get to keep your edits even if you update K2.

If you tried the other way you would have to backup and re-patch K2 after every update.

I wanted to use template overrides to change the correct file and in the correct LOGICAL place.

Placing this code into a random place in a file that doesn't deal with the generation of the og meta tags, IS a hacky way of doing it.

It would make more sense to to edit the relevant code that generates the meta tags, in the relevant file (using a template override obviously), rather than just placing it in any old place in the item.php file.

But I suppose I like to keep my code neat and logical. Other people may not.

Exactly

Some people help you with your project for free while other may don't.
Anyway it works like this.

Either hack core files or change item.php
No other file can be overriden.

I am locking the topic now.