Saaame issue as me, just got an X-E3 second hand yesterday:
Camera is in EYE SENSOR + LCD IMG DISPLAY view mode
when first turned on, the LCD image shows
when moving it up to my eye, the image switches to the EVF
when moving away from the EVF / camera, the LCD does NOT turn back on till I turn it off and on again
when turning off and on again the LCD displays correctly. Repeat.