Can I just sign "break" without signing "time"?
Yes! In many contexts, simply signing "break" (sliding your hand between your fingers) is enough to communicate that you are taking a rest or pausing an activity.
Why don't we use the sign for breaking an object?
ASL uses different signs for different meanings of the same English word. The sign for breaking a stick is a physical action, while this sign specifically means a pause, rest, or intermission.
Does it matter which fingers I slide my hand between?
Usually, the dominant hand slides between the index and middle fingers or the middle and ring fingers of the non-dominant hand. As long as it clearly wedges between the fingers, the exact placement is flexible.