Squeeze juice from half the grapefruit and reserve. With a small, sharp knife, cut peel from second half, down to flesh (discard peels), then cut between inner membranes to release half-segments into a small bowl.
In a blender, whirl grapefruit juice, miso, rice vinegar, and sake until smooth.
In a 1- to 2-quart pan over medium heat, melt butter. Add shallots and ginger and sprinkle with salt and pepper.
Stir often until shallots are limp, 3 to 4 minutes.
Pour in miso mixture and stir until sauce is bubbling and slightly thickened, 2 to 3 minutes.
On a plate, mix flour, thyme, oregano, and salt and pepper to taste. Coat scallops in mixture.
Pour oil into a 10- to 12-inch nonstick frying pan over high heat and tilt pan to coat. When hot, set scallops in pan, spacing evenly. Cook, turning each scallop once with tongs, until golden brown on both sides and opaque but still moist-looking in the center (cut to test), about 4 minutes total. Transfer to a serving plate.
Pour miso mixture into frying pan and stir, scraping bottom of pan to release browned bits, until bubbling, about 1 minute.
Pour sauce around scallops and top with reserved grapefruit segments and the chives.