They face Portugal, Spain and then Turkey over the next few days at the competition in Poland, after knocking out holders France in the qualifiers.
Despite his achievements to date however, Gemmill faces an uncertain future, saying: “You look at the last two years and I would defy anybody to have done a better job.
“I never have been on a permanent contract, just on a tournament-to-tournament basis.
“You would like it to be confirmed, but football like life is very fickle, so you never know."