GuardTrails
What it means
This is not a rest day, and the word matters: it is not about tiredness but about diminishing returns. Too long a run of full days ends up devaluing the days themselves. After ten or so full days (order of magnitude), the site is beautiful and you look at it thinking about something else.
If the programme provides no break, the break happens anyway — at random, on a good day you end up wasting.
"No plan" does not mean "nothing". Beach, bikes, a market, a nap. What matters is that no decision is pending.
In a capital, it is the aimless walk that follows the two hours with a guide on the first day: see Two hours with a guide, then we walk.
Where it goes
A few such days on a long trip, about a week apart (order of magnitude), never two in a row. A long run of full days with no break is the signal to watch for. And the place must let you get out without driving: a day with no plan spent driving towards something is not one.
An example
Across seven nights of rest by the sea, it took a day and a half before the group started organising trips inland (our trips). Six people who had explicitly asked for rest.
Beyond a day and a half, rest stops resting: it creates a need for activity. That is why days with no plan are spread out rather than stacked.
A break can also land in the right place without being planned: in Jūrmala, the day of beach, bikes and bog came on day twelve of twenty-one, and nothing else in the programme suggests anyone had worked it out (see Jūrmala is not a spa town).
What it does not say
The day-and-a-half threshold is a parameter of the engine, set per traveller, not a rule. Yours may be three days — and you know it: it is the moment you start looking at what's around.