I guess I'll take a try at guessing some things about how this transformer might be designed. I've never actually had an xray transformer in front of me, but I know a little about transformers and I think I've picked up a little more about these from hanging around this forum for a few years. All of this is guess work, so hopefully Duncan can prove me right or wrong with an ohm meter and maybe some other tests later.
First, to aid the discussion, I copied the three pictures from the original links, reduced their size to not waste space here, and I'll include these here, now.
So it looks like we have two coil sections on opposite sides of a common circular(-ish) metal core.
Another member was recently working on a different xray transformer. For that one he had a pretty good schematic of the transformer in its circuit. The transformer basically had two high-voltage secondary sections. I forget the exact numbers but let me guess that the tube was driven by 70 KV across it. This was made by the two secondaries both producing 35 KV (out of phase with each other). So the bottom end of each secondary was tied to ground and also tied to the other. So the hot HV end of each secondary was making 35 KV relative to ground but because they were out of phase, the voltage between them was the sum or 70 KV. Just to be clear, by out of phase, I mean when one HV output was at the peak of its AC wave the other output was at its minimum. Looking at the connections on this transformer I think it might be built in the same dual secondary way. I think you said it should be a 60 KV transformer. That would mean 30 KV on each secondary If my guess is right.
Let's go with the assumption that the output has two secondaries in series with the common center point at ground potential. I think picture 1 makes sense as the high voltage output. Why are there 3 connections on the left-side coil? I think any xray tube would have a filament on the cathode end. On the left side, two wires are the same color (yellow), so I would guess between these two yellow wires are a very few turns to produce a low voltage for the filament across them. They are wound on the outside (HV) of this coil so they don't have a problem with insulation from ground -- the filament voltage is floating at 30 KV relative to ground. The red wire then would be the cathode (-) 30 KV. So that (in my view) makes the white wire from the other coil the anode (+) 30 KV output.
The transformers only make AC outputs. The implied (-) cathode and (+) anode potentials are derived from the AC, either by external diodes (as I will show in my later circuit sketch) or because an xray tube with a filament is essentially a vacuum tube diode that will automatically only pass the AC potential, that is across it, in one direction.
So in picture 1, I think the red wire is one HV output from the hot end of one secondary winding. If I'm right the white wire on the other coil would be the hot end of the other secondary winding. But where are the opposite ends of each secondary that I think should be grounded? In picture 3, there are two black wires on each coil that are cut off. These are toward the top of the picture and under the plastic housing of the transformer. The picture is cut off so we can't see where they are coming from but they must be out of the coil sections. Where did they go? Who knows? There is a circular pattern in the plastic. Maybe there is a hole in each circular pattern they could have passed through; maybe they just came out through the square holes where other wires are passing.
Why were they cut? Ask the guy who cut them. My guess is that they passed through the center of each circular pattern in the plastic (which we can't see in the picture) but that was the easy way to get the transformer out of the tank that used to hold it. Why are there two wires on each coil? Although we can't see in the picture my guess is the two black wires that are cut on each coil both come from the same connection. Why are there two? Possibly redundancy safety on the grounding of the HV source.
Now, let's think about the primary side coil(s). In pictures 2 and 3, there seem to be wires coming out of the coils, through the square holes in the plastic and connected to the terminal strip. I think these are the primary connections. It looks to me that each coil section has the same number of wires coming out, and with the same colors on each coil. So I would guess each coil section has its own primary windings and these are probably in identical configurations on each coil. From a manufacturing point of view, the coils would be made the same except in the last step where one coil would just get a single HV output wire, while the other coil would get a slightly different HV output wire, plus a few separate turns to make a coil for the filament voltage.
So I suspect that these primary wires coming out of each coil section will have the same configuration. For one thing, this could allow selecting 110 V or 220V input by either connecting coils of the two primaries in either series or parallel. So how are the primaries configured? There are a couple hints. Looking at picture 3, there is a terminal strip with 8 connection points. Counting from left to right, the coil wires coming to pin 2 and pin 6 seem to actually be two wires in parallel. This probably means it is the center tap of two serially connected coils. As Bob pointed out, the blue thing at the left of the terminals is probably a thermal switch for protection if the transformer gets hot. It looks to be in series with the black primary wire out of the left-side coil and terminal 1. I would think this means the black wire is AC input to one end of a coil.
There is an odd thing that I haven't quite figured out. Looking at picture 2, terminal 4 is the white wire from the left-side coil. This is wired to a strap around the middle of the core (possibly ground?) and it also goes to a 10K fairly high wattage resistor that then connects to terminal 7, that is the connection to the white wire from the right-side coil. So far I can't guess what this resistor might be doing.
Some smart ohm meter readings are needed on each of these primary side coil connections to figure out what's going on.
Here's a sketch I made of what I think the basic transformer looks like and the wires coming out of it. From the photos, I can't be sure if all the orientation is right -- maybe the way I drew the HV wires, the primary wire should be coming out the back side in my drawing. But that doesn't logically affect what is going on.
And then I made a crude schematic of how I think this may have been connected with an xray tube.
I think the general orientation might be right, but I clearly don't have the primary coils right because I have one too many terminals on each side vs. the wires out of the coils. I was just trying to get the general idea of how I think it might be configured.
Hopefully Duncan can figure out how to prove, with an ohm meter, if I am close or not. One part will be getting access to those black wires that are cut off inside the plastic case to see if they are the other end of the secondaries, as I have guessed.
Hope some of this makes sense and helps.