When signing up for a GLL tournament you need to pick which players from your team you want to represent you. If you get a message saying you have no eligible players, it is because:
One or more of your players are signed for another tournament of the same type (Eg. already signed for Wingman NA when trying to sign up for Wingman EU.)
One or more of your players have not picked a country in their profile on play.gll.gg
Always make sure all of the players you intend to put in a team have all their profile information filled in correctly on play.gll.gg.