Bring vinegar, ¼ cup water, sugar, and kosher salt to a boil in a small nonreactive saucepan over medium-high. Boil, stirring often, until sugar is dissolved, about 1 minute. Remove from heat, and add cherry tomatoes. Let stand 15 minutes. Drain tomatoes; discard pickling liquid. Thread 1 cherry tomato half and 1 bread piece onto each of 12 (4-inch) metal skewers.
Preheat grill to high (450°F to 500°F). Place all pintxos on oiled grates. Grill pickled-tomato caprese pintxos, uncovered, turning often, until bread is lightly toasted, about 2 minutes. Grill shrimp-and-speck pintxos, uncovered, flipping once, until shrimp is cooked through and speck is beginning to crisp, 2 to 3 minutes. Grill pork belly pintxos, uncovered, brushing with honey and turning occasionally, until pork belly is glazed and crisp in spots, 8 to 12 minutes.
After removing pintxos from grill, sprinkle pork belly pintxos with shichimi togarashi. Thread 1 mozzarella ball and 1 basil leaf onto each pickled-tomato caprese pintxo, and sprinkle with sel gris. Serve all pintxos immediately.