Make the jerk-rub marinade:
Whisk all of the ingredients together in a bowl. Store in an airtight container for up to 3 months.
Season the shrimp:
Place shrimp and olive oil in a large zip-top bag and shake to coat. Add jerk spice mixture and shake again to coat thoroughly. Set aside and prepare glaze.
Make the rum and brown sugar glaze:
In a small saucepot, combine lime juice, rum, and brown sugar. Bring to a simmer, then reduce heat. Add the cornstarch mixed with water and bring back to a simmer while continuously whisking. Glaze should simmer until it is thick enough to coat the back of a spoon.
Grill the shrimp:
- Thread shrimp and pineapple cubes onto bamboo skewers that have been soaked in warm water, about six or so shrimp per skewer.
- Grill shrimp skewers over medium-high heat while brushing with the rum and brown sugar glaze until shrimp are cooked through, about 2 to 3 minutes per side.