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According to this Wikipedia article, the bodily movements you describe were first noted during the First Great Awakening in the 18th Century, in Protestant Europe and the British colonies.
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That behavior is generally tied to the receiving of "gifts" from the Holy Spirit, as it is the kind of thing a person naturally needs to do to get attention during a service when The Spirit has taken hold and the recipient is thus unable to communicate normally. This is in fact very old behavior, although modern Pentecostals have been the main force reviving it in the modern era.
Some of that is actually right there in the writings of Paul, which are the oldest Christian writings we have, dating to about 55CE. So it appears to have started very early indeed.
Paul's very first letter shows there was already a nascent sectarian divide in the congregation in Corinth based on evangelists, (Particularly himself and Apollos), and in worship behavior, which he called "gifts".
The ones he listed were
...and then he later adds his own gifts of "hope" and "love".
Ironically, it rather reads like he's attempting to curtail most of this behavior, without out and out banning it. Perhaps flat out banning tongues could well have been a politically untenable position within that body at that time, so he was trying to wean them from it. Regardless, he flat out bans any tongues without interpreters, and goes on in the last chapter to advise everyone to instead strive for the gifts of faith, hope, and love, particularly the latter.
Point being that this kind of thing likely actually goes back to at least the first half century of the Christian era.