I know not everything in pool obeys geometry. There’s physics too with rail compression and spin. But I think this is still the gist of why it works and that at least gives you a sense that there is an ideal distance and what that is and why…
Let's talk about what works and what doesn't and why. Let's say you have a known three rail track to the corner pocket and a fly on the wall identified that works.
That works because you've picked a fly that aligns with where the third rail pocket is projected outward as if the tables were mirrored into space.
And that mirroring reflects as a certain path of bounces and reflections on your actual table. Keep in mind your initial fly position is slightly different than the mathematical fly position because you're adjusting for speed, rail compression, and running english.
And you can use that same fly for a different cueball position...
...because your fly is in the same corner pocket in the mirror space.

And that results in a series of bounces and reflections into the intended pocket. So it works. Most advice is to pick a fly at least 4 feet from the table. But now you realize there is actually an ideal distance that is 1 imaginary table further and 2 imaginary tables over from your target. So table size can be a factor. And if you pick a spot too close or too far away, it's not going to work.
So yeah, let's say you have an established new fly for three railing to the side pocket.
That's projecting to the side pocket in mirror world, instead of projecting to the corner pocket.
And that's a series of bounces and reflections leading to the side pocket on your actual table.
So sure, use that same fly from a different starting ball position. That projects out to the same side pocket in mirror world.
So now you do have a new path of bounces and reflections leading to the side pocket on your actual table. Keep in mind, the ideal reference distance to the fly is a little shorter than it would be for corner pocket three rail shots.
Also these angles are a little sharper so sometimes the rail compression and running english will fight you even more. So it's no shock you'll find this to be inconsistent.