Last year, Google said that Android's "Check for update" button would be fixed to actually pull an update if there was one available for your phone. Google then said a few months later that the button was broken but that it'd be fixed in 2018. Now it looks like the button is indeed working.
Google Play Services version 12.2.09 appears to enable the "Check for update" button. The update isn't rolling out to the public quite yet, but it is available in beta. You can get it by joining the Play Services beta on the Play Store or by side loading it from APK Mirror.
Google hasn't officially announced that Play Services v12.2.09 fixes the "Check for update" button, but many people that've installed it on their phones have had success pulling the February 2018 update.
It can be super frustrating when you know that there's a new update available for your phone but hitting the "Check for update" button doesn't pull it down. That's why it's great to see that Google is finally making the button work for its device. Now when there's a new feature or security patch that you want, you should be able to snag it right away.