When should Beginners finish a Game of Go?
Under Chinese scoring (AKA area scoring), you can (and with new players should) play until each player has no move they can make.

There is no downside under Chinese scoring for a player to play stones into untenable positions, nor is there downside for a player to defend a position inefficiently (so long as they don't fill in their eyes).  As a result, a new player should try to attack any area they think they can and you should attack them on any area you can, even if those areas are too small to build a live group.  This will help them get a more concrete sense of why certain groups are alive or dead, understand what territory can or cannot be viably contested, and learn how defend their own groups from attack without losing their eyes.

For these reasons, I actually recommend Chinese scoring for new players.  In addition, I believe it's easier for new players to understand.  Japanese scoring requires players to understand the concept of territory, which is much easier once a player has played several games.  The overall strategy and techniques of Go are not substantially affected by which scoring system you use (it mostly matters in terms of endgame play), so learning to play under Chinese scoring should not be an impediment to later learning Japanese scoring.  See What are the difference between Chinese and Japanese rules in Go? for more information.