Optician used to tell me to work the muscle by following my finger to my nose, trying to maintain a single image. At a certain point it will snap into two - the 'lazy' eye has given up and drifted slightly - the goal is to get the finger as close as possible. Obviously if you get very close or all the way, that's 'cross-eyed', but I just can't do it.
Here is what worked for me. I used my laptop, zoomed in a bit on the images and brought the screen fairly close to my face. I ensured that the image was crisp using each eye (I also have astigmatism, and I probably also need reading glasses, but there is a sweet spot where both eyes have good focus, and I ensured I was there.) While crossing my eyes a bit, I start to see a third image in the center of the two images, but it's either out of focus (like two overlapping images), or it's very thin, like it's not the full image. I relax and keep my attention on this imperfect image and try to focus on it without trying too hard. Using this approach the image suddenly comes into focus and I no longer have to try to keep it there.
I feel like the key might be to notice the very beginning of the desired image in the center and then to try and focus on it, but in a bit of a relaxed way.
Incidentally when it works it is extremely weird! The other images essentially disappear and it's like you've travelled to another dimension.
I have otherwise good vision, I can read small text from farther than most people (I didn't realize not everyone could read all the small letters on an eye test), I don't have a problem seeing things up close either, etc. but I lack the ability to properly cross my eyes for some reason.
It's too bad because I've spent a decent amount of time at bars with those spot the difference machines lol
Zoom the images in front of your eyes so that they are little less than same width as your eyes.
Try to look behind/beyond the image, as in let your eyes loose/relax. Don't stare at the images instead see in that direction as if you are day dreaming.
Images will overlap at one point. If they don't completely perfectly overlap, reduce the zoom.
Once they overlap, focus the overlapped image.
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Method 2: Use kitchen towel rolls
After putting those images in front of you, make a binocular out of used kitchen rolls.
Point each roll to each image.
There you go.
Put the pair of images in front of your eyes.
Bring your finger between your face and the image.
Now look at your finger.
Move your finger back and forth.
While doing this, notice that at a particular distance, the images in background will perfectly overlap each other.
That's your moment.
Pull out your finger and look at that image.
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Should take lot less tries to learn doing it without finger. I have taught cross eye to my siblings and cousins using this method. But if you always need finger to focus it's fine.