I would try another HDMI lead, inspect sockets and plugs, especially in view of the intermittent nature.
The specs tell you whether there is switchable graphics. I can't find that specific model, you tell us.

The Device Manager will show two under Display adapters if it has two.
However that is not relevant.

In Control Panel > Devices and Printers, will show external monitor.

The switch is for an external monitor, not specifically HDMI.