I've never had a zombie, much tried to mix one myself. It looks like a remarkably-complicated drink. You can find its history and the two alleged originals recipes here. Excerpt:
From the end of Prohibition to the dawn of Disco, the Zombie was the world's most famous drink. It kick-started the whole Tiki craze, and put Don The Beachcomber's Hollywood bar on the map. Inventor Donn Beach kept his original 1934 recipe a closely guarded secret – and when the Jeff finally found it, the recipe was in code! While sipping samples of vintage Zombie recipes, you'll learn why this legendary drink was the toast of the Hollywood movie crowd, and hear the true-life detective story behind how the recipe's secret code was cracked.