Since I host with Netlify, I've written a lightweight Netlify function that looks at my Pinboard account for changes. If there are changes, it simply re-runs the static site build. During the build, Lektor, the static site generator, runs a custom plugin I've written that generates the link blog page from the Pinboard API.
Definitely more work than it was "worth", but as a person who doesn't get to write lots of code every day, it was a blast putting it all together.