Speculating without much of anything in particular to base anything on:

My brain can't give the commands necessary to "follow the rhythm," because somewhere between the sound coming in, and the action going out, it's the command gets scrambled.

Action wanted:

1. Ear detects sound.
2. Ear communicates with brain.
3. Brain recognizes sound
4. Brain sends command to muscle.
5. Muscle reacts to do something at next time sound is expected.

"Hear" produces "Tap"

Problem is that the communication between step 3 and 4 is broken. The part of the brain that sends the command to act does not associate it's activity with a communication from the part that "hears."

Or the part of the brain that hears does not associate the hearing with a need to communicate something to the part that controls action.

Speculation:

1. Brain sends command to muscle.
2. Muscle reacts to do something that produces a sound.
3. Ear detects sound.
4. Ear communicates with brain
5. Brain recognizes sound.

"Tap" produces "Hear."

The same cycle, but starting at a different end.

Perhaps a practice in which you "turn the sequence around" would allow you to reinforce some association between the parts of the brain that recognize the sound and the parts that instruct the action. (????)

Instead of "hear" produces "tap" - which isn't working,

Could you practice "tap" produces "hear"

with any expectation that practice might develop an improved coordination (association) between the brain parts that hear and the brain parts that act?

A practice might consist of doing something that

1. requires a muscle action
2. you can feel the action
3. the action produces a sound
4. you can hear the sound
5. when you hear the sound, you repeat the sequence

At first practice, it shouldn't matter whether "rhythm" is achieved, as long as you can repeat the sequence to form an association between tapping, feeling the action, hearing the result, and tapping again. The goal would be to get all the parts to work together, at first without worrying about rhythm, but eventually so that the connections work in both directions:

Tap => Hear, or Hear =>: Tap.

I have absolutely no reason to believe this might help, but to me (demented as I may be) it sounds like it might be a reasonable thing to try (if any of this is intelligible enough for anyone to figure out how to try to do it(?)).

John