Nice to see at least some agreement
[on closing non-dominant eye] Yes that is what I am seeing; one image disappears and the other stays where it is, let's call it image A
[on closing dominant eye] Absolutely not; one image disappears and the other stays where it is, let's call it image B - Just as I'd expect it to
Images A and B are, of course, in different places relative to the background.
I think what is causing the difference between us may well be the question of which (of a pair of 'double fingers') one is lining up with the distant object, but I'm not so sure of the reason - but it could be that my dominant eye is much more 'strongly dominant' than yours. I say that because when I 'line up my finger with the distant object' I think that it is invariably the 'finger image' seen by my dominant eye that I line up with the distant object. If one does that, then closing the non-dominant eye leaves the (now just one) image still aligned with the distant object, whereas if one closes one's dominant eye the image left is not still aligned with the distant object (thereby giving the impression of 'a jump').
If one started by lining up the image from the non-dominant eye with the distant object, then everything would obviously be different.
What a load of rubbish, The mere fact that you make the statement negates much of what you have been describing, the finger may appear to jump sideways - In reality Image A visible in one eye will disappear when that eye is closed and image B visible in the other eye will appear.
I think you're quibbling here - a 'jump' is what is perceived although, as you say, one is switching from seeing the image from one eye to seeing the image from the other eye.
This takes it straight back to the non focussed point appearing to show as double image with both eyes open. A situation which you admit to seeing, except you keep denying it. So which is it; do you see the non focussed point as a double image or not?
The confusion about what I 'say' results from the fact that I often struggle to see the 'double image' (although I can usually eventually succeed) - again perhaps due to my having a 'very strongly dominant' eye (doing its damndest to 'suppress' what is coming from the other eye.
What confuses me most is the apparent conflict between all these discussions and my historical experiences. You obviously have to take my word for it, and it was a very long time ago, but, as I've said, I have in my time administered this test to countless people, and I really can't recall any significant 'difficulties'. In general, people just seemed able to tell me whether alignment of things 'changed', or didn't change, when the closed each eye - and they almost invariably reported 'change' when they closed one eye but not when they closed the other one.