I've a pre_get_posts filter with a check for main query and search, in this check I add a meta query:

$meta_query = array(
  'relation' => 'OR',
  array(
    'key' => 'exclude',
    'value' => '1',
    'compare' => '!=',
  ),
  array(
    'key' => 'exclude',
    'value' => '',
    'compare' => '=',
  ),
);

$query->set('meta_query', $meta_query);

I've tried a couple of ways for 'NOT EXISTS' with the key exclude, but to no avail.

However the output I am getting for this seems to be an excessive nested set of joins. Dumping the query from the global wp_query I get the following:

SELECT SQL_CALC_FOUND_ROWS DISTINCT wp_posts.ID
FROM wp_posts
INNER JOIN wp_postmeta ON (wp_posts.ID = wp_postmeta.post_id)
INNER JOIN wp_postmeta AS mt1 ON (wp_posts.ID = mt1.post_id)
LEFT JOIN wp_postmeta ON wp_posts.ID = wp_postmeta.post_id
WHERE 1=1
  AND (((wp_posts.post_title LIKE '%exclude%')
        OR (wp_postmeta.meta_value LIKE '%exclude%')
        OR (wp_posts.post_excerpt LIKE '%exclude%')
        OR (wp_posts.post_content LIKE '%exclude%')))
  AND ((wp_postmeta.meta_key = 'exclude'
        AND wp_postmeta.meta_value != '1')
       OR (mt1.meta_key = 'exclude'
           AND mt1.meta_value = ''))
  AND wp_posts.post_type IN ('post',
                             'page',
                             'attachment',
                             'cpt_people',
                             'cpt_history',
                             'cpt_case_studies')
  AND (wp_posts.post_status = 'publish'
       OR wp_posts.post_status = 'acf-disabled'
       OR wp_posts.post_author = 1
       AND wp_posts.post_status = 'private')
GROUP BY wp_posts.ID
ORDER BY wp_posts.post_title LIKE '%exclude%' DESC, wp_posts.post_date DESC
LIMIT 0, 9

Now if I manually build the query in SQL I can get the results I expect, however WordPress seems to be creating excessive joins for wp_postmeta and the result is an error:

Not unique table/alias: 'wp_postmeta'

Removing the first join:

INNER JOIN wp_postmeta ON ( wp_posts.ID = wp_postmeta.post_id )

manually with the query returns the expected results.