That is not what is described as the virtual mouse mode. The documentation shows that then virtual mouse mode is activated, an on-screen prompt appear showing the possible actions in this mode. This is certainly not happening in my case.
I verified tonight that when I use L1+R3, virtual mouse mode is actually entered and I can exit that in the normal way. That is however certainly not what I am seeing when my originally described problem occurs.
It is true that the mouse pointer somehow appear on-screen when my wierd problem occurs. This happens while I am not aware that I am in any way touching either the touchpad on the keyboard or the touchpad on the controller.

For the moment I have turned off virtual mouse mode in the settings because I am not using that. My belief is that this will however not be the solution to my original problem.