Slaughtering (including Kosher or Halal)

[Cal]

3)The dead body should be allowed to stop having convulsions before cutting the body up as the movements indicate that the parts of the body still have life giving oxygen (that the blood provided just minutes ago).

That is the correct procedure, but the reason is because if the animal is still convulsing, it looks like it is still alive. If people would start butchering animals while they appear to be alive, the result would be that they would start butchering animals a moment earlier, when they haven't died yet. (If a Jew does kosher-slaughter on a kosher animal, the waiting period until the end of the convulsions is not technically required, but it is highly recommended.)

How important is point three, that the body should have no convulsions?

It is an actual prohibition if the convulsions haven't stopped, but there is no liability to earthly punishment if that is transgressed. The prohibition against severing and eating the meat while the animal is still alive is much more severe.

I understand that meat which is cut from cattle after the heart has stopped beating can twitch even long after. Does the term "convulsion" include any little visible twitch? Or does it rather refer to big walking movements? Thanks a lot for your help! I have the chance to ask some local butchers, but since the definitions of someone unfamiliar with the Noahide Code might vary from my understanding, I want to be as thorough as possible when I ask them.