What does the phrase somewhere between 8 and 12 seconds mean?
We often speak of numbers as if they were on a physical scale, like a ruler or yardstick. In that sentence, a range of time, a duration, is being expressed spatially, and so you find the phrase somewhere between, which means at some location that is found between those two (temporal) points.
The word somewhere means "at some location". The exact location is not specified. It is intentionally vague or indefinite.
He would be polite for a brief time, approximately 10 seconds, give or take a couple of seconds, and then he would say how he truly felt.
P.S. I don't mean to imply that the speaker visualizes a ruler, but that we easily transpose time into the linear. We speak of timelines and say things like "It happened at some point between last Thursday evening and now".