Was thinking about this recently. The author misses the importance of timing in the unity of perception. It would be rather easy to conduct an experiment and ask people, “did X and Y happen at the same time?” where X and Y are different stimuli. You could test over a variety of different senses and time differences to determine if people are integrating their experiences or not.
The other important element is attention and awareness. You can certainly be focused on one thing more than another—this can be a useful kind of disunity
Here's an interesting experiment you can do around retrospective perception and timing: clap your hands once, listening for the sound of the clap. Notice what it's like to remember the sound of the clap for a minute or so. Now, clap your hands twice, again listening closely and noticing what it's like to remember the sound for a little while. In the second case, is it possible for you to remember the sound of the first clap only, without an echo of the second?
The other important element is attention and awareness. You can certainly be focused on one thing more than another—this can be a useful kind of disunity