In my experience it is very rare for there to be a period at the end of boarding where the gate is still open, but no or few passengers are in the process of 'settling in'. This usually only happens if the flight is delayed at the last minute or if they keep it open for a passenger who is late to the gate (don't be that passenger!) who has checked in luggage that would need to be removed.
Usually, as soon as the 'rush' settles down, that is that. Typically, this is around the time when the flight is scheduled to depart. You could try to time your arrival at the gate to be around 5 minutes before departure, this will typically not be a problem.
However, doing so is disrespectful. If you are delayed on the way to the gate you could wind up delaying several hundred other people, just because you didn't want to stand in line for 5-10 extra minutes. Those people certainly do not enjoy sitting in those seats for an extra 5-10 minutes, waiting for you.
If not standing in line is this important to you, buy a first/business class ticket and avoid the queue. Otherwise, show consideration for your fellow travelers and arrive at the gate in a timely manner and try to board the plane as efficiently as possible.
You can, of course, seat yourself outside the gate and read/watch movies/listen to music/whatever until you are just about the last one there. Just be at the gate in a timely manner.
Sorry if this sounds a little harsh. I've just been in this situation too many times, where a plane full of people have to wait as much as 15 minutes because someone couldn't be bothered to get to the gate on time. In busy airports this delay can be compounded due to the flight missing its takeoff slot and having to wait for another one to become available. Ditto on the other end of the journey. Holding up the flight for 10 minutes can sometimes delay it up to an hour.