I think the key is not "going cross-eyed" as much as it is relaxing your focus until the images merge. If you intentionally cross your eyes, it hurts. If you de-focus/relax your eyes until the images merge, it doesn't hurt.
That's more for traditional "magic eye" pattern stereograms where you want to relax your eyes to look off into the middle distance behind the subject instead of intensely focusing on something unnaturally close to your face.
i had the same thing where best i could get when i relaxed was a narrow merge, and when i crossed my focus was too close to my face to be helpful, plus strain.
sudden clicked after fully crossing 5 or 6 times and then relaxing and was able to hold the "3rd image" very easily. felt like magic, even hardest difficulty was obvious
For me it just does not work right now. Maybe I have bad eyesight, I wear glasses and am past 40. I believe I was able to do this trick in past though. At the very least on psychedelics (various kinds). This also made me able to relax my eyes more, wheras I normally have too much pressure on them according to optician.