I’ve further tested gates at LFPG, YMML and YPAD and am yet to find a gate that will provide more than one pushback direction.
The first gate I tried at default YMML, B21, is set as "Both", offers me Left and Right direction (and straight)
The first gate I tried at default YPAD, Gate 3, is as "Right", offers only Right direction (and straight). Gates from 4 to 10 are set as "Left", and they gave me only Left (and straight).
I tried changing Gate 3 to "Both" and, sure enough, it gives me both directions, even if in this case, Left wouldn't make much sense, since it will end up in a direction opposite to the most logical to take off, so the parking was correctly set to Right by default.