Joe: I think the lyrics you posted make a bit more sense if lined up this way:

CHIAPENECAS (Mexican Dance Song)
(Lyrics: Eleanor Graham Vance)

Down in Mexico, joyous Mexico,
Where the evening star shines brightly,
You can work away through the sunny day,
But when starlight comes there is dancing, ay, ay!
Down in Mexico, joyous Mexico,
You will learn our old time dance;
Ev'ry happy pair will be light as air
While you dance along like this: (clap hands)

Sing to the music I play (clap hands)
Whirl round your partner this way (Clap hands)
There's not a chance to go wrong, (clap hands)
If you will dance to this song (clap hands)

Ay! Ay! Singing and whirling,
Ay! Ay! Swinging and twirling,
Ay! Ay! Come and join In our song.
Join the crowd! Come along with us.
Ay! Ay! Singing and whirling,
Ay! Ay! Swinging and twirling,
Ay! Ay! Come and join In our song.
Join the crowd! Come along, OLE! (Clap hands)