To monitor nodes' healthiness, there are tools for Bitcoin and Ethereum (e.g. https://github.com/cubedro/eth-net-intelligence-api). Some of them are tools that sends heartbeats representing an uprunning node.
Currently, for Stellar-Core, I set
PUBLIC_HTTP_PORT=true, and my firewall limits that port from external access.
Other than tuning firewall policies, is there any other way / tools for external parties to check my node healthiness?