As chief of the ADITYAS he also manages solar affairs. But never mind bright shiny globes in the sky. He is much more interested in the whole rain, water and justice thing, and seems happy to delegate sunny responsibilities elsewhere.
VARUNA is really concerned with the dark side. (If you didn’t realize the sun had a dark side, you’ve been paying too much attention to scientific fact.)
He rules the domain of night — the dark celestial ocean — and presumably keeps a careful watch on the Sun as it travels from evening’s west back to morning’s east.
Meanwhile, he is busy keeping law and order in collaboration with MITRA the God of Oaths. He watches over all; the stars in the sky are his sentinels, peering down at the Earth like a billion security cameras.
According to later representations, he wears a cloud cloak, rides a tortoise and carries a noosed rope. This all seems about right for the twin responsibilities of Water and Justice.