"There is no void--all is full of His nearness," wrote Nicholas Arseniev in Revelation of Life Eternal.
And I think that there is no such thing as "filler," the ontological equivalent of the styrofoam peanuts used in packing.
There are no dead or meaningless/worthless moments.
Does this fact demand, then, a kind of hypervigilance on our part, as that of an eyeball staring starkly open at all times so as to not miss anything?
No, we can rest when need be, because the meaningfulness of each moment comes from God.
"He who keeps you will not slumber. Behold, He who keeps Israel shall neither slumber nor sleep" (Psalm 121).