It is imperfect like all analogies, but let's take a toy example to clarify what I think. Let's say you are going to start something in 3 months, a new job or maybe you want to finally get in shape. If you think that your energy, will, and desire are like fuel in a slowly refilling tank, you might want to stop what you are doing now to save the energy that will have to be spent in 3 months.
I remember years ago, when I was a serious sportsman, we had a few days off at Easter. And I rested. I came back flat, dead, without energy.
Now the flywheel accumulates energy when the motor to which it is connected is working. The flywheel stores energy during the expansion phases (the combustion phase in an ICE) of the engine to return it during the passive phases.
Which, going back to the dilemma "when you have long-term down time, you have energy available to do other work, for networking, etc.," if the flywheel analogy is the right one, it means that you store energy to spend when there is down time by doing work, not by turning the engine off for days or weeks.
If no work is done for a certain period of time (the motor is off), the flywheel does not accumulate energy to spend, it is dead, needs time to accumulate energy again.
If you don't go to the gym one or two days after a period of serious training, which may be a week or a month, the training session is likely to go well. If the rest period, "I'm so tired, I need a break," is longer, say two weeks, you are likely to come back not invigorated, but flat, without desire, you may think about putting it off for another two weeks because you still feel tired, the tank has not been filled with fuel, you may think. But it is because energy, will and desire work like a flywheel.