The thing about shrimp—and this goes for the grill or the stove or the oven or wherever—is that it’s extremely easy to overcook. More than a couple of minutes is often too much. I like shrimp at the point where they’ve just lost that translucence, where they’re still pliant and not yet firm. That’s hard to get. It’s a feel thing.
Always, always take them off the pan or the stove or the grill before they’re done—well before. As I said, it’s a feel thing, but you want them to have a slight translucence. They’ll continue to cook from the heat they’ve built up, eventually taking on that just-lost-their-translucence look you want. It’s a little like making scrambled eggs: By the time they look done in the pan, they’re ruined, because they’ll harden and become rubberized on the plate.
On the grill, my advice would be to go and get some banana leaves. They’re a staple in Vietnamese cooking. Salvadoran cooking, too—tamales are typically wrapped in them.
I’d marinate the shrimp for a short time—let’s say a mixture of lime juice, fish sauce, some sugar, rice-wine vinegar, cracked black pepper, a bit of grated ginger, some chopped garlic, maybe a drop of Sriracha—then set them atop a couple of soaked banana leaves (soaked so they don’t burn) and cover the grill. Give it 8 to 10 minutes. You won’t get char, but you also won’t get overcooking. What you’ll get, and what you want, is the smoke, which will indirectly cook your shrimp.