I like to think of things like yoga, meditation, and prayer as a messy abstraction layer for controlling the parts of your body you normally can not. Created over millenniums of black-box reverse engineering by people of different levels of skill and honesty who are not sharing their results. One of the things guided meditation, and hypnotists will do is have you purposely relax each muscle group one at a time. Though for a specific twitch, that really depends on what is causing it.
I wish there was more skeptical, but open minded research into ancient practices. It seems it's all either people who blindly believe in their flavor of magic, or people who go in assuming it's nonsense and miss the step between the action and the result.
To put it more succinctly, mind over matter is enough of an issue that we have double blind studies to account for the placebo effect.
Trying to work out why this would be difficult, since it doesn't seem to be, so my first assumption ought to be that I'm doing this wrong.
If I point in front of me I can twirl my pointers in a circle such that they go in opposite directions. This seems to be the most intuitive and trivial, because both are actually doing the same movement (inward and outward at the same time). I can also twirl them so they spin in the same direction, this seems only slightly more difficult, but if I just think of them as tracing the wheels of car it's trivial.
Then again, I've never had any trouble patting my head and rubbing my stomach either.
Then point your index fingers toward each other so that they are both tracing the same wheel. They can each go forward or backward. Most people struggle with making them go opposite directions. To the point that they'll do it once or a half of a time, and then switch directions with one hand and not even realize it. It's fun to teach kids.
You can do it with your whole hand, or arm, or just the fingers, with different size circles, each takes a bit of practice once you get over the initial hurdle.
If I imagine the wheel over my head (as if the wheel axle was vertical), or in front of me but the axle going forwards (wheel is moving left/right), I can do the opposite circles just fine.
But if I imagine the axle going left/right as you describe, it takes extra cognitive effort. If I imagine drawing circles, I can't do it. Instead, I have to think of each axis of movement separately. In my mind, I'm not thinking "Draw circles in the air", but rather, "Move fingers forward and back, while moving arms up and down".
The end result is the same, but what's happening in my mind to get there is totally different.
I normally just ask a group of kids "hey can you do this?" then after I explain that it's different directions, watch them laugh as they try to do it.
Ok … 2 days, 23 hours and 57 min of training yet.
spoiler alert:
The secret for me is to realize the fingers are on the same spot at the same time twice each rotation.
Your question are about different things than that, and the first one is about a different thing than the second one.
Learning to move a particular muscle you don't normally use consciously (like moving your ears or your nostrils) is indeed a matter of practice. Sometimes all it takes is getting conscious that there is a muscle there, and then you improve your feedback loop between sending a command and feeling it move.
But a muscle that uncontrollably twitches is a whole different process. For instance some muscle cramps are related to dehydration or lack of certain minerals. So the cause can be more chemical than nervous system (ie coming from the nervous system).
PS: I have no particular expertise in this area.