A friend and I discussed yesterday whether ‘perpetual activity’ is simply a function of my work and life stage – or is it my underlying temperament. In a previous conversation, he put to me, that the ceaseless activity I observe in my daughter might suggest ‘the fruit never falls far from the tree’.
I think of myself as basically liking my rest. I’m just not allowed any. My family all seem to feel me sitting down means they need to spur me to action. Sitting down for them is me signalling a desire to be reactivated. I routinely stay on my feet at home, to keep them from ‘tasking’ me further.
Similarly at work, keeping busy is my way. If things are in good order, I instinctively seek some ‘new’ things to make happen – at times to the chagrin of those around me.
I blame the Emperor Vespasian as quoted by Montaigne in his essay ‘Against Idleness’ which I read the other day:
The Emperor Vespasian, being sick of the disease whereof he died, did not for all that neglect to inquire after the state of the empire, and even in bed continually despatched very many affairs of great consequence; for which, being reproved by his physician, as a thing prejudicial to his health, “An emperor,” said he, “must die standing.”
A fine saying, in my opinion, and worthy of a great prince. The Emperor Adrian since made use of the same words, and kings should be often put in mind of them, to make them know that the great office conferred upon them of the command of so many men, is not an employment of ease; and that there is nothing can so justly disgust a subject, and make him unwilling to expose himself to labour and danger for the service of his prince, than to see him, in the meantime, devoted to his ease and frivolous amusement, and to be solicitous of his preservation who so much neglects that of his people.
Never sitting down and avoiding any whiff of ‘ease’ or ‘frivolous amusement’ in my domestic and working life have become habits. We are what we repeatedly do. Just need to keep standing.
Achilles & Aristotle 
Aren’t you ignoring our good friend and guide Aristotle here in your pursuit of M Montaigne?
“Happiness is thought to depend on leisure; for we are busy that we may have leisure, and make war that we may live in peace.”
Yes but:
The Romans… sometimes also… purposely maintained wars with some of their enemies, not only to keep their own men in action, for fear lest idleness, the mother of corruption, should bring upon them some worse inconvenience:
“Et patimur longae pacis mala; saevior armis Luxuria incumbit.”
[“And we suffer the ills of a long peace; luxury is more pernicious than war.”–Juvenal, vi. 291.]
but also to serve for a blood-letting to their Republic, and a little to evaporate the too vehement heat of their youth, to prune and clear the branches from the stock too luxuriant in wood; and to this end it was that they maintained so long a war with Carthage.
Albeit wrong for our day, excessive Luxuriance requires our regular attention, as we know.