On many small island countries, import duties are the only source of national revenue. Customs officials are concerned that you are going to sell the equipment
without paying the duty. To varying degrees, they are also looking for drugs depending on the country. Jamaica has a serious drug problem, so they are looking
real careful there.
I found it's best to act like a dumb tourist whenever dealing with customs (this is a feat which comes natural to me).
If you have a native of the country you're visiting waiting for you, I believe it's worse if customs knows that.
They may assume that person to be your connection to fence your equipment.
I had no trouble with customs here, but out of 9 guys coming in with equipment, I was the only one. Being able to produce a license often helps
(whenever possible I always try to get my license in advance).
Bribes and payoffs are a way of life in Jamaica. When all else fails, you might give it a try. You have to be very careful, there is as much of an art to
presenting green as there is to stuffing it in one's pocket. Be very discreet. Don't give it to the first official who questions you with a crowd around,
wait until they take you aside. If you and/or your equipment land up in customs jail, sorry, you shouldn't have listened to me.