Yes, the 14-inch is on a fixed pier. If I have to travel, my experiment will probably not happen. C'est la guerre.
Now, the question of parallax is a curious one. In theory, there is no need for a reference image taken months in advance (or later); one can simply measure the positions of stars in the eclipse image and compare them to positions from a good astrometric catalog, such as Gaia DR3. I took a series of images recently, at night, so I could verify that this combination of camera + lens would provide images of sufficient precision to detect the very small gravitational deflections. It appears to work well enough, so I can go ahead with my plan without having to make any changes to the equipment.
If one did want to compare directly the positions of stars in a pre-eclipse image with those in a during-eclipse image, it wouldn't matter much where the pre-eclipse image had been acquired. Yes, a very few stars -- those closest to the Earth -- would shift their positions due to the motion of the Earth around the Sun during the time between the images. The parallax due to a different location on the Earth's surface would be completely dwarfed by that due to the motion of the Earth around the Sun. The parallactic shift would be, in almost every case, smaller than the shift due to the Sun's gravity. Moreover, one could compute the size and direction of the parallactic shift, and correct for it.
I wouldn't recommend doing the direct comparison. Eclipse image positions vs. catalog is the way to go, in my opinion.
Thanks for that! Although things like parallax and such are things many of us have heard of it is always nice to learn from people who really understand it, because knowing how the numbers pan out and/or become negligible is another level of 'knowing' which most of us either haven't the mathematical skills to follow or simply just haven't had the need to do more than read about it, never having had the need to take it into account in practice.
Also, I later remembered why my brain was nagging me about differing geographic positions and parallax, it was a barely half remembered thing about astrometry for close approach asteroids and some of the recent impactors, and as you know distance matters.
I may have also conflated it with stellar aberration which I have never fully understood because I think that is something that needs a mathematic understanding over a metaphorical one. [I remember years ago Richard Feynman in a televised interview refusing to give a simplistic metaphor for magnetism, despite being famous for describing complex issues in lay terms when needed. They said can't you do it with elastic bands or something, he said no, it can't be simplified like that]. Then there are the old PEP photometry issues of air mass and refraction and all that which many people may have forgotten about as CCD can make those irrelevant a lot of the time (for small fields), all the potential optical equipment aberrations too if wide field imaging. I don't envy anyone attempting this, even if many things are irrelevant you've to know enough to know what is and isn't relevant!
My memory still works, but it tends to get mixed on what thing applies to what other thing at times, or either confuses or conflates things.
One example on memory is that I remember reading somewhere (long ago) that half the deviation was due to special relativity and half due to gravitational redshift, but I could have got that confused with Mercury's nodal recession. I think that's right though, about an arcsec total with about half an arcsec due to each.
Another is that sometimes people made noises about Eddington having fudged things, due to lack of time for taking the exposures, inability of the equipment of the day, and not having taken a statistically meaningful number of observations to be a valid sample size. I think I read of that one in quite recent times after someone dug out his original plates and demonstrated that yes, he was right, yes it worked and was doable with the plates taken and no he did not fudge. I think the lack of other expeditions' ability to catch the eclipse in 1919 is sometimes also cited (ie no independent confirmation).
And, the memory tickles, he may have had some luck as to what stars were near the Sun then, given that the "best" astrometric catalogue in those days was probably Boss's General Catalogue, a mixed bag compilation. He'd none of our lovely allsky or big chunk of sky catalogues good to 1 arcsec (or even better if you ask GAIA).
It'd be nice if some of you guys managed this experiment, even if unsuccessful in terms of end result. I shall try to remember to look back in around then.