Ultralight aircraft pilot reported engine failure in downwind leg of traffic pattern. Pilot returned and landed immediately.

Narrative

After a touch and go on Runway XX; I climbed out normally; turned right crosswind; then turned downwind. Upon completing the turn into the right downwind; the engine (Rotax 912ULS) sputtered; then died completely. I quickly requested priority; then established best glide speed at 55 kts. Since I had just begun the downwind leg; I quickly judged that if I was to glide straight ahead; I might be too low to be able to successfully turn 180 degrees and land on Runway XX. So; instead; I turned to the right 90 degrees; added 10 degrees of flaps; flew a base leg; and then turned left towards Runway XY. I was high; and I knew I would have a tailwind of about 10-14 kts (straight down the runway); so I added 10 more degrees of flaps (20 is max) and slipped the plane to lose altitude; heading straight for the Runway 'XY' numbers; maintaining 55 kts. When I was low enough; I released the slip and flew straight into a downwind landing. The landing was very smooth; though a bit fast as expected. I used the brakes to slow down; and turned at the first available taxiway. My momentum carried me across the runway threshold; where I announced over UNICOM that my landing was successful; that neither I nor the plane were damaged; and that the active runway was clear.Sitting on the taxiway; I quickly discovered that both fuel valves were in the 'off' (horizontal) position. I remembered that just previous to my last touch and go; I had noticed that the right tank fuel level was significantly lower than the left tank; and so I shut off the fuel to the right tank hoping to equalize the levels. Before doing so; I did not check the position of the left tank valve lever; which is located right behind the pilot's left shoulder; and takes some effort to see or feel. I assumed it was open when I closed the right tank valve; but actually; it was closed. The engine dying was my fault; I had starved the engine of fuel. Upon opening the fuel valves; the engine started immediately and ran normally.