I can't help you directly, but I suspect that the car is the property of the Jamaica Railway Corporation which ran the island's public railways until the last one closed in 1992. The JRC still exists, mainly to administer the remaining assets of the railway and because it leases a few short sections of track to bauxite mining companies who still operate freight lines in the island. I have found these contact details for JRC:
Mr. Mr. Harold Brady - Chairman
Mr. Owen Crooks - General Manager
142 Barry Street,
Kingston.
Tel: (876) 922-6443
Fax: (876) 922-4539
Email -
odcrooks@cwjamaica.com
The JRC introduced diesel railcars in about 1963 but this carriage seems to be much older. I suspect that a few old passenger cars were retained after the diesel railcars were introduced, possibly for 'tourist' specials or maybe to run additional trains at times of exceptional demand. But all this is just speculation on my part...