How does one fit in a fleeting glance of awakening with the rest of their lives?
Rather, how does one fit in the rest of their life with that fleeting glance. At any rate there are several possible outcomes: it can serve as inspiration, can be dismissed or even forgotten.
So it may or may not have a great impact.
Depends on one's preparation, sincerity and deep intention. In other words, depends on how tied up to ego-mind one is.
Any other options?
The continuity of that awakening could be established even if, on the surface, one is unaware of it.
How can there be a continuity of something that is discontinuous at the same time?
There could be an abiding certainty that doesn't depend on constantly experiencing or attempting to experience. An inner knowing or confidence that the awakening process is abiding and it's our awareness that phases in and out.
You mean faith or belief?
I mean a state of watchfulness, vigilance over ego-mind's machinations. Allowing a knowledge of the heart that's not swayed by spurious doubts and arguments.