I find that there are different techniques to seeing both.
If I stare at the image and cross my eyes until focus lock I get crossview where the image goes back into the page.
If I bring the image right up to my eyes and stare through it into the distance, then slowly move the image backwards into my gaze until I get focus lock, then I get parallel view where the image pops out of the page.
I have always wondered the difference between the two and why it happens. Thanks for shedding some light on it :)
EDIT: I have just managed to achieve both without moving my head or the image for the first time in my life! Just by trying to look further 'past' the picture into the distance, and then by slightly crossing my eyes and focussing at a point in front of the picture.
I have been trying to do this for 30 years, and it is only your explanation which helped me to do it. Thanks so much!