Of course it needs to be vertically centered. The center of the lens needs to be at the same altitude of the water levels in the water device. Otherwise you are looking slightly upwards or downwards at it. A very small angle misalignment with the line of sight of bodies in the foreground creates a very large angle numerous miles away.
No.
This seems so simple to me. I don't know how to explain it to you.
The camera has a field of view. Okay? Changing the pointing angle won't change the height or the angle between the camera lens and the water level. Height and angle remain the same. The angle of incidence of the ray from water level to the lens changes. Yes. But that won't alter the geometry. If it alters anything, it'll alter the optics, like distortion or clarity or focus, but none of that will have any bearing on what we're after here, particularly at the minute incident angles involved.
And before you start saying it does, if you were inclined, that's a separate issue from what you are saying, about changing the viewing angle or relative heights. That's a flat "no," and unless you can comprehend this basic point, I don't know how we can even have a discussion or analysis about the rest of the test.
Here's what I do. I set up the apparatus first. I spend most of my time on that, and only because I'm trying to get it square and level for the purposes of the perspective element of the demo. If I didn't care about that, I could just throw it on the mount and not worry about level. The water will level itself. But I won't be able to use the lines of perspective of the cube. The cube will no longer matter.
But because I want it to, I level the whole rig left/right, forward/backward. And it's an ordeal, especially when there is wind buffeting. I can't use the plumb bob in the wind, and the plumb bob is proven to me to be the most sensitive to departure from level. But I still use the spirit level and the bubble level on the tripod used to hold the rig.
As for the water levels in the tube? I don't care if they're filled so that they are exactly center on the cube. For convenience, I make sure they're filled so that they fall somewhere between the middle space. Because that's the range of freedom of have with my horizontal guide line. If I'm not going to bother sighting through the cube, I don't even need that. I'll just line the tubes up. But the sight line allows me to move the camera off angle from the tubes yet maintain level with the tubes.
I make sure the guide line is level by, after aligning it with the water level miniscus (love that word) on one end, measuring the height of each end to 1/64th of an inch. I also eyeball it and if it doesn't look right, I'll double and triple check until not only does every level match but my eye agrees. I work my way around, checking it along each side of the cube.
Once that's all done, I measure out 3 feet from below the cube tripod and set up the camera tripod. I get it roughly at the same height, mount the camera, and then start finding the actual level height. I zoom in on the water level and try to match up with the guideline. I pan across the guideline. I tilt up and down. I zoom out, zoom in, fine tuning the height of the camera on the tripod. Once I feel good about the height of the camera, I lock it in. Now, the camera is level with the water, as long as I don't bump or move the tripod.
But I can still pan, tilt, zoom...and none of that will change the level height relationship.
If I have to move the camera in the tranverse, like line up with the tubes or line up so that I can shoot through the cube, I have to check level height again and adjust if necessary. But once I have it level, I can pan/tilt/zoom and it doesn't effect the level relationship.
I choose to frame the picture using pan/tilt/zoom depending on the aesthetic or the point I want to focus in on. But there's no requirement that I lock the camera in at all degrees of freedom just to try to get an image with the same amount of space above and below the level line. That's ridiculous.
If there's some ocular reason why a miniscule degree of angle of incidence to the lens centerpoint is critical for this kind of test, at this kind of focal length such that the light from the water tube alignment needs to be entering the lens and hitting the camera sensor at precisely 90°, I have no idea why that would matter. It's a false fear that any distortion from that kind of off-axis viewing through the lens would cause the level lines to be untrue.
You're not even saying that. At least not yet. You're just confusing what impact certain degrees of freedom of the camera will have on the observation. If need be, I will take images of the same setup with only the camera pitch changing. And I'll show you have the water level alignment will not change, whether I'm pointing the camera down from level or up from level. As long as I'm not changing height of the camera, all that's doing is changing the field of view.