Almost certainly the colourful James "Dun" Hay (1881-1940), who captained the then two best teams in the world at start of century. Fell out with Celtic over money for new contract, went south, even did a stint of war service as gunner in WW1. Played football for Ayr Utd and later managed them, was banned sine die for refusing to apologise after accusing a club official of trying to bribe a ref.
Not sure Jamaican link but by 1880s plenty of Jamaicans and other AfroCaribbeans came to Scotland, espec Edinburgh Univ to train as doctors, etc.