How will wearing an eyepatch correct binocular double vision?

Not really. Correct it, but it will make the double vision disappear when the patch is in place. Double vision is caused by the eyes pointing in different directions giving the brain two images. Covering one eye gets rid of one of the two.
Removes one image. Patching removes the image from the patched eye - no more seeing double. It does not fix the underlying problem (discoordination of the eye muscles).