“Besides, just by an energy equivalence analysis, atmospheric pressure cannot drive a work process in that manner. Gravity-based potential energy by way of the relative difference in liquid levels, is the main source of energy causing the flow.”
The problem with that is the reason you are “Siphoning” is because in order to get the liquid from the higher spot to the lower spot, you need to get the liquid from the higher spot a little bit higher first.
In order to do that you are decreasing the pressure in the tube (relative to the pressure pushing down on the top of the liquid) in order to bring liquid to the high point in the tube, where after the force of gravity will keep the pressure in the tube at its lesser state by itself (which continues to draw more liquid uphill.
If it was in a vacuum, there would be no way to force the liquid to defy gravity and go up, either to start the process, or after the process got started. You are relying on differential pressure between the atmosphere and the tube to make the liquid go “uphill” first.
If you could not pre-fill the "down" tube, getting it started would be a problem. Remember the atmosphere is pushing up on the open end of the down tube (or down on the lower reservoir) just as much as it's pushing down on the upper resovoir. (Yes there is a tiny fractional difference, but it's in the wrong direction, the lower reservoir or the open end of the down tube experiences slightly higher atmospheric pressure, because there is more air above it.)
Now if the upper reservoir were sealed the at the top, then the pressure above it would decrease, compared to the pressure pushing up on the open end of the down tube, and that differential would tend to counter the weight of the water in the down tube, and the siphon would at some point stop.
Here is a good way to explain it.
You have a glass of iced tea. If you drink it without a straw you need to have the glass higher than your mouth and tip it and its all gravity.
If you use a straw, you can drink it with your mouth higher than the liquid. You use suction from your mouth to lower the pressure between the straw and the atmosphere pressing down on the top of the tea, which allows the tea to “defy gravity”. If you tried to drink the tea in a vacuum, you could not do it with a straw because you could not suck greater than vacuum.
So a siphon requires both gravity and atmosphere. Remember you need to suck on the siphon to start it (ie raise the height of the column of liquid)...once the liquid passes the high spot, it starts falling down the other side, which continues the sucking by itself.