Heat gas or charcoal grill. In medium bowl, beat dry pudding mix and milk as directed on box (milk amount is slightly less than called for on box). Let set up 5 minutes.
Meanwhile, remove pie crust from pouch; gently press crust in bottom and up side of 8-inch cast-iron skillet, leaving crust overhanging edge of skillet.
Add pineapple, rum and 1/2 cup of the coconut to pudding; stir until well combined. Spoon into crust. Sprinkle with remaining 1/2 cup coconut.
Fold crust edge over filling, pleating as necessary and leaving filling uncovered in center. Brush crust with egg.
Place skillet on grill over medium-high heat. Cover grill; cook 10 to 14 minutes or until crust is golden brown. Cool slightly before serving.