Continuing Part 1, in addition to the timbre, whether the pitch interval between the high and low tones affects the perception of the illusion is also of interest to me.
In the original example, the difference between the high tone and the low tone is an octave, that is, the pitch interval is 12 semitones. Their pitch names are the same.
Firstly, let's do an experiment. Modify the pitch of the high tone to test the effect:
If you haven't done the hearing experiment, please click the link to participate.
According to the results of the questionnaire, there are different senses of hearing at different pitch intervals. The results can be roughly summarized as the following:
When the pitch interval is large, the result is like what described in Part 1. Most people feel that the high and low tones are separated into sides (the left and right are not necessarily). When the interval drops to around seven to nine semitones, the situation becomes complicated. Some people feel that the high and low tones are mixed together and there is no longer the feeling of separation of high and low tones into the left and right, while on the other hand, some people perceive different sounds between their ears. For example, one of their ears might perceive the same as the actual signal, but the other ear only perceives the high or low tone as if part of the signal is picked out.
This phenomenon may have something to do with the operation of the left and right cerebral hemispheres. The left hemisphere controls the right half of the body, and the right hemisphere controls the left half of the body. Of course, our ears are no exception. The phenomenon observed in this experiment is consistent with many common rules in the music world. For example, conductors usually use the right hand to indicate the beat, while the left hand is used to indicate the musical expression of the piece. In chorus, the higher registers usually stand to the right (seen from the direction of the members) and the lower registers to the left, so that they can hear each other well . The melody part of a song is generally presented in high pitch. Most people can easily remember the melody, but they may not remember the performance of other musical instruments. The above examples also show that the human brain can extract part of the music we hear.
Although rumor has it that the left hemisphere is good at processing logic and details, neuroscience has never confirmed that the functions of each hemisphere can be so simply defined. From the results of the above questionnaire, it is impossible to conclude that the left and the right hemisphere can be certainly defined as rumored, because the tendency of left and right directionality perceived by subjects is not completely consistent. However, some tendencies of the two hemispheres are well-known. For example, language ability and speech impairment are mostly related to the left hemisphere. When we notice an abnormality in semantics and syntax, there is a brainwave (ELAN, Early Left Anterior Negativity) appearing in front of the left hemisphere, indicating that we have noticed this abnormality. When we hear unexpected notes or chords (such as a sudden appearance for a note outside the tonality of the music itself, which is similar to the feeling of noticing "a wrong note"), a brainwave (ERAN, Early Right Anterior Negativity) appears in the front part of the right hemisphere. The reaction time of these two situations is similar, and both seem to be generated in the Broca area. This fact indicates that there is a similarity between music and language. 
I cannot be certain of why the results of this experiment appear to be consistent with the common rules in the music industry. I can only speculate that the brain has a particular principle on processing any sound signal including languages, sounds, and music. The sound signal of this experiment may be processed by our brain as language to some extent, so there is a phenomenon that the same signal heard in both ears appears to have different perceptions. Our brain is suspected of trying to extract details and messages from the signal so that we can understand.
When the pitch interval is within three or four semitones, the proportion of the subjects who perceive intermittent high and low tones, i.e. as same as the actual signal, increases significantly. In this situation, all the tones sound to be mixed together and there is no longer the feeling of high and low tones being separated into the left and right ears, because the sound frequencies become so close that we treat them all as the same group. This phenomenon is related to the "grouping effect", which will be discussed later.
 Deutsch, Diana. Musical Illusions and Phantom Words (p. 44). Oxford University Press. (2019)
 Koelsch, Stefan. Brain and Music. John Wiley & Sons. (2012)