Custom calculation of wp_term_taxonomy Category “count”

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WP does not include Privates Posts in calculating the “count” field of any particular Category record in Table: wp_term_taxonomy, even if there are Private Posts in that Category. I would like to override this so that Private Posts ARE include in the count. Where/How is the “count” field calculated? I’m comfortable modifying MySQL, but those changes are likely to be lost in an upgrade.

So, alternatively, is there an action/function I can add in my Child-theme functions.php to force the display of Categories that are only associated with Private Posts?