Method
In a small bowl, stir together garlic and oil then let stand 15 minutes.
With a mandoline or other manual slicer, slice squash crosswise into 1/16-inch thick rounds, transferring to plate.
Remove plastic wrap from 2 pieces of rolled-out-pizza dough and lightly brush dough with some garlic oil. Trying not to stretch dough, carefully transfer it, oiled side down with your hands to rack of grill. If it's a very hot day, the dough may get too soft to transfer easily; if so, pop it into the freezer until firm again, about 15 minutes.
Lightly brush top with some garlic oil. When grilling pizzas, rotate them if one side of grill is hotter than the other. Grill crusts, covered, until undersides are golden brown on bottom, about 4 minutes. Flip crusts over with 2 metal spatulas and top each crust with half of cheeses, squash, and thyme. Lightly brush pizzas with some garlic oil and grill covered for about 5 minutes or until undersides are golden brown and cheeses are melted.
Garnish pizzas with thyme sprigs and cut into wedges.