The Americanism rambunctious, possibly brought to us by Irish immigrants seems to be a variant of the British term of equivalent meaning, rambustious.
The latter, it is suggested, may have been coined from ram plus bust.
To ram, of course, is “to butt, strike,” and generally to behave in the manner of a frolicsome male sheep.
The earliest recorded use of the verb, which has been traced to the early thirteenth century, is in the sense, “to beat, thrash.”
This sense still exists, as in the colloquial, “I’ll bust him in the nose!”
So if we have a man, or especially a small boy, in boisterous mood, ramming around and busting people, he may certainly best be described as rambustious!