As a Flight Engineer I have faced forwards and sideways depending on aircraft type and phase of flight. As for horizontal, never when on duty unless I was mending something, although I have been the only one awake in the flight deck on occasion!
As to the P3 in your question, some operators used pilots trained to operate the F/E panel and they were variously known as Second Officers, System Panel Operators, etc., but not Flight Engineers as this is a specific license and requires several years of practical aircraft engineering experience.