The Songs from Trinidad with Dulcie is Edric Connor's 1958 book. Correction- pages 68-69. I will scan the sheets to Joe, perhaps he will be kind and make a midi.

Quoted from a reminiscence of Trinidad:

"I am often asked to compare the children of yesterday with those of today. While many of yesterday's girls sang "Dulcie in the Moonlight, Dulcie in the dew, Dulcie never came home, until the clock struck two," and lamented the disposition of a fabled Dulcie, there are all too many real Dulcie's today, not merely in Trinidad and Tobago but the world over, who are the dispair of their parents."

"Memories of My Childhood," George Allyene.
Printed in Trinidad & Tobago's Newsday, December 26, 2007.
He mentions games, but refers to "Dulcie in the Moonlight" as a hauntingly sad song, not a dance or game.

Perhaps the dance-game is later than the song. I can find no further information.