What is the official rule on alternate team members?

There is no "official" rule on "alternate" members.  Alternates may participate only if one of the 15 regular team members can't make it the day of the competition or if a team member becomes ill or injured. Alternates may not fill in if there is a schedule conflict or if the schedule changes on the day of the competition.

Some tournaments restrict the number (if any) per team and sometimes allow them to participate in trials events and drop off impound items. Many tournaments issue and require "regular" team members to wear "hospital style" wrist bands so alternates do not "accidentally" cover for a late member.