Agency owners: what earns a local business a place on your follow-up list?

Building KlirProspect has raised a useful question: finding contact details is one step, but deciding whether there’s a good reason to reach out takes more judgment.

A missing website field doesn’t prove a business has no website. A failed check doesn’t prove the site is broken.
For those pitching restaurants and cafés, what makes you move a business from “worth checking” to “worth contacting”?
A visible website issue, a referral, a recent business change—or something else?
I’d appreciate one concrete example, without naming the business. I’m using this feedback to refine how KlirProspect presents candidates and supports follow-ups.