Does Neocities support anything like webhooks, so people can do normal workflow of pushing to GitHub and having it be auto-deployed. Or even pushing to a Neocities remote would be fine too. I currently use a Raspberry Pi server that uses webhooks and it's very nice.
It doesn't have webhooks, but it has a full API. You could use CircleCI or another build tool to publish your site when you push to GitHub. This way you also get more control over the build process and can use tools other than Jekyll.
There's an API right now. Github webhooks are coming, as is git push support. They were sidelined to facilitate the infrastructure upgrades so we could provide more bandwidth and storage. We'll get back to them.