It means "eye-like" as in the spot on a stingray that makes it appear to be looking at you.
As far as I know, there are no words for nose-like or even ear-like.
We're hardwired to be aware of eyes. We want to be seen, we're afraid to be seen, we need to be seen.
The very best way to engage with your customers is for your organization to develop some more eyes. And the empathy to use them. Not to spy on us, but to see us, understand us and treat us the way we want to be treated—like people.