I forgot that the E-m10 mark II has two types of video out (either to a HDMI monitor using the HDMI cable or to the old analog video format using the yellow RCA connector with the CB-AVC3 cable). In older Olympus cameras, just plugging in the CB-AVC3 cable turned off video on the monitor, as the camera believed it was using an external monitor.
If you have an appropriate HDMI cable, you might try just plugging the cable in and see if it turns off the display.
Unfortunately, it appears Olympus no longer supplies either the CB-AVC3 or an HDMI cable with the E-m10 mark II. I don't recall off hand, what type of HDMI cable the E-m10 mark II has (full size, mini, micro, etc.).
You probably want to look at pages 101, 110, and 111 in the fine manual.
If you want to get fancier without removing the CB-AVC3 cable, this post (in polish, use google translate) shows how to mod the cable so it has a switch that enables video or not, and use the USB and/or shutter release at the same time:
An alternative method might be to enable the wifi interface. But it might not be as helpful, as wifi takes some amount of power as well, and you have to also power the tablet/phone to keep the connection going.
Note, the CB-AVC3 won't work on the newest Olympus cameras (E-m1 mark II, TG-5, E-PL9, E-m10 mark III) as Olympus has moved away from its 12-pin combination cable that was introduced back in the E-500 time frame. However, the E-m5 mark II and anything newer should now have live view to HDMI, so that may be an option (it depends on whether just plugging in the cable turns off the monitor, or if you have to really connect an HDMI monitor).