wonder if we should call this keepAliveInitialDelayMillis to better indicate what it actually does? https://nodejs.org/api/net.html#net_socket_setkeepalive_enable_initialdelay

I could not find a way to delay accepting a new TCP connection in node.js. If the socket is not listening, then the OS will refuse the connection immediately. I have an other idea that I will have to test: creating the server in an other process and blocking the event loop with busy waiting.

Edit:
Tried it, did not work. I'm unsure if it is even possible to reliably delay accepting connections in node.js, I do not know its internals well enough.

Maybe mocking the socket with something like this could work, if that makes any sense.

I think that con.once('end', () => { also should have clearTimeout(connectionTimeoutHandle), use case:
connectionTimeoutMillis set to some value.
Application receive SIGTERM or any other shutdown signal, because client still not connected we can not call client.end(), so application can call client.connection.stream.destroy().
If destroy will be called with error, then error event will be raised, connectingErrorHandler will be executed and timeout connectionTimeoutHandle will be cleared. Everything OK.
If destroy will be called without arguments, clearTimeout(connectionTimeoutHandle) will never happened and applucation will be hang up while timeout will not be called.

Why we can not call client.end():
Current end code:

  if (this.activeQuery) {
    // if we have an active query we need to force a disconnect
    // on the socket - otherwise a hung query could block end forever
    this.connection.stream.destroy()
  } else {
    this.connection.end()
  }

Because activeQuery is undefined while client is not connected, connection.end() will be called, which itself implies opened connection, because write data to socket.

You are correct; the timer should be cleared in that event handler too.

To make sure I understand your use case, are you calling client.connection.stream.destroy() in your signal handler if the connection hasn't been established yet, or is there another way to trigger this behavior?
And passing in an error, e.g. client.connection.stream.destroy(new Error('SIGTERM')) is the workaround?

Currently I do not call stream.destroy(), but I'd like modify application, because hang up is not cool.
stream.destroy(new Error(...)) is workaround, yes. But from other side, destroy called from client.end called without arguments... (which will not work actually in current case, just as example).

I did some testing just to confirm.

Calling client.end() before the connection is established seems to wait for the connection to succeed (in which case the timeout will be cleared). There will be no activeQuery before connecting successfully.

Calling client.connection.stream.destroy() (without an error) will reject the client.connect() promise with a Connection terminated unexpectedly error and wait for the timeout.

Calling client.connection.stream.destroy(new Error()) (with an error) will reject the client.connect() promise with the passed in error and not wait for the timeout.

The only way to make the application hang on this timer is to call client.connection.stream.destroy() from your own code. And the solution is to pass in an error.