The reason you have not received a satisfactory answer to your questions is because they are too vague and require a lot of unknown/ implied knowledge/ back story to answer; you might as well ask… how would I build an AI?
Has the AI be instructed to tap?
Is the AI listening too music?
Is the AI bored?
It would also obviously depend on the design of the AI; a better starting point would be why do humans tap when listening to music?
Do any of you guys have any background/understanding of the motor coordination system behind this?
Again this is a complex system that involves topics like ‘free will’, consciousness, motor neurons, muscle groups, etc.
When you think; the words you mentally use in your internal dialogue cause micro inflections in your larynx. When you imagine or plan a motor movement; all the muscle groups that will be involved in the action again also show/ receive micro inflections. This shows that the human nervous/ motor system is not a simple on/ off schema but a complex analogue gradient that can be influenced/ affected by any/ all mental processes.
When someone in a meeting/ conference starts tapping it’s because they are usually bored. The brain craves constant stimulation; if the complexity/ level of the overall ‘thought pattern’ drops below a certain threshold the brain uses/ exhibits coping strategies to stimulate it’s self; this is part of the system that stops you falling asleep at inopportune moments. Lack of stimulation can cause many such outward phenomena and in extreme cases causes the constant pacing/ rocking of caged animals etc.
Usually depending on where you where born and raised you will have an innate sense of rhythm for the type of music you were exposed too when young. This not only influences your music tastes but because the majority of the tunes had a local/ similar overall rhythm/ beat all your listening/ learning of the tunes where mapped using the same neural area to represent that rhythm/ beat. This makes that particular rhythm have a very strong influence on your neural processes when you hear that beat, you are sub consciously generating learned patterns for all the songs you know with that beat. This extremely strong neural pattern influence is registered by the whole nervous system and is expressed by strong micro inflections; you just want too dance or at least tap your foot or finger.
It’s also no coincidence that the base rhythms most cultures use in their music directly mirrors the brains base operating rhythms/ frequencies
I could go on but I presume you get the gist.
