If you look at the list of positions which can be used to meet the position of responsibility requirement for Star and Life, you will see that assistant patrol leader is not listed there.
Life Leadership Requirement
National Youth Leadership Training (NYLT) is an intense week long leadership training class for youth
Life is the rank a Scout can earn after Star. A Scout working on Life continues to develop leadership, participates in service projects, and earns merit badges.
A Scouts BSA Troop is actually run by its youth leaders. See the list of Scouts BSA youth leadership positions.
The Den Chief Service Award recognizes Scouts and Venturers who serve a Cub Scout den for one year, are trained, and are active members of their Troop or Crew. The award is a red, white, and blue cord, which is worn on the left shoulder under the epaulet. A certificate is also available.
Scouts who are progressing toward the rank of Life must continue to show leadership, either by taking a leadership position in their unit or by doing an approved leadership project.