When signing up for a GLL tournament you need to select which players from your team you want to represent the team in that specific tournament. 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.) or one or more of your players have not picked a country in their GLL profile.
Always make sure all of the players you intend to put in a team have all their profile information filled in correctly on their GLL account.
Submit a request if you have further issues with selecting your team.