Mix gluten-free pancake mix, water, egg, buckwheat flour, and vegetable oil together in a bowl until there are no lumps. Add additional water if needed to thin batter. Let batter sit for 15 minutes for fluffier pancakes.
Heat a lightly oiled griddle over medium-low heat. Pour 1/4 cup batter onto the hot griddle and cook until golden brown, about 2 minutes. Flip and cook until opposite side is golden brown, about 1 minute more.