OM-D E-M10 II LCD not working when EVF auto switched on

As pterosonus said above, its possible that dirt on the Electronic View Finder (EVF) surface may obscure the eye sensor, giving a false signal that your face/eye is against the EVF and so the camera will display through the EVF only. Its also worth checking that you haven't inadvertently set the menu option to EVF display only (The EVF auto switch function), although your thread title implies you have checked this!

This thread caught my interest as I had a similar issue with my E-M10 mk2 in December 2017. The (EVF) did not work automatically when I looked through it . It allowed manual switching between the screen and EVF view (using the button pterosonus mentioned), so I knew the EVF itself did actually work.

I noticed that if I folded the LCD tilt screen out and back in again the automatic switching between EVF and screen worked intermittently, so I believed this is where my fault was; the camera somehow was sensing that the tilt screen was open/tilted - even when not, hence the automatic switching between screen and EVF did not work.

This was confirmed by gently thumb pressing the lower right or left hand corner of the closed LCD screen (as if to ensure the screen was closed). When doing this the EVF auto switch function worked fine.

Fortunately mine was still covered by Olympus warranty and I was able to describe this issue in correspondence to them. I hope this makes sense and that you get it sorted.