'jamaica' refers to the rum, not to a place or to a person.
One of the balms of Gilead!

I've got some good old jamaica in my liquor cabinet now. I should dig it out and toast old H. T. Bryant; several of his songs still live in one form or another, especially on college campuses.

There is a Peach Blow farm in New Hampshire, some excavating is being done, dunno what for. Pumpkins are grown there.
Which reminded me that a pumpkin once was used to mother 'stump rum.'

Ah, superb jamaica from Appleton. www.appletonrum.com
Their Estate rums rank with a good single malt (not a 15-year old of course).