Click on home button through iOS gateway and vnc access

Is it possible to send the home button command for an iOS device accessing it via VNC provided by iOS Gateway?

Yes.

PressHomeButton
See the documentation on mobile testing commands.

Sorry, why was the answer rejected? It’s the answer. It’s the engineered mechanism for doing what was asked about.

I would like to click the home button using VNC client. The iOS gateway runs a VNC server on the device allowing to “remote control” it via a VNC client, like RealVNC. The question is: How can I send this PressHomeButton command using the VNC client?

You can't do it using a generic VNC viewer. That functionality is built into Eggplant Functional -- it requires special hooks on both sides of the connection. You can do it with Eggplant Manual, which is freely available.