I'm confused how this was possible in Jamaica given the fact that whites made a tiny minority of the population, and the slave population was a whole lot larger. It also does not seem to be a claim I have heard very often of slavery in the British/french Caribbean.
There's a slight misreading you've made there (though it's a very understandable one). What Petley is saying is that half of the enslaved population did not work on sugar plantations. Now, whilst the popular impression of the British Caribbean is one of a series of never-ending sugar estates, the economy of Jamaica is rather more diverse than that. In addition to sugar, coffee is also grown in significant quantities on Jamaica during slavery; you also have plantations growing food for domestic consumption, including and particularly raising livestock (although Barbados is the exceptional food producer of the British Caribbean before slavery's abolition). In addition, some slaves would work primarily in the island's infrastructure industry or in the service economy, whilst others worked in agriculture but not in any particular field (the 'jobbing' gangs; groups of slaves hired out to work on plantations that needed additional workers).
This was the approximate distribution of slave labour in 1832, just before the abolition of slavery in the British Caribbean:
| Economic/ labour activity | Approx. no. of slaves | Percentage of total (rounded) |
|---|---|---|
| Sugar growing | 155,000 | 50% |
| Livestock and staple foods | 60,000 | 19% |
| Coffee growing | 45,000 | 14% |
| Urban work | 25,000 | 8% |
| 'Jobbing' gangs | 20,000 | 6% |
| Pimento growing | 3,000 | 1% |
| Wharf/dock work | 1,000 | 1% |
| Other | 4,000 | 1% |
| Total | 313,000 | 100% |
| ^Source: ^B. ^W. ^Higman, ^Slave ^Population ^and ^Economy ^in ^Jamaica, ^1807 ^- ^1834 |
So although only about 50% of slaves on Jamaica were working on sugar plantations, a solid 90% were working within the wider plantation economy; at least two-thirds were mainly growing cash crops for export, and well over 80% were probably working on a fixed plantation or farm estate (not all farms are plantations, it should be noted; small farms exist in the Caribbean just as they do in the US). So you are very right to have been sceptical of the claim that half of all slaves did not work on plantations or estates in Jamaica, it's just that the source you cite means to refer to sugar estates specifically which, whilst by far the dominant force in the economy and usually the largest estates, were not the only kind of plantation or farm estate in Jamaica.