We all know the importance of having the right hook when you email someone asking for a link. One of the hooks commonly talked about is finding something that is broken on the site you are contacting.
Run Screaming Frog over the site you’d like to get a link from and filter the results by 404 pages, then see where these pages are linked to internally. Then reference these in your outreach email. This will help distinguish your email from the other emails they get that look auto generated and spammy. The fact you mention something like a broken link shows you are a real person.