Or a day-night-day-penumbra-umbra-penumbra cycle. The primary-facing side would get maximum light just before entering the penumbra, experience total darkness in the umbra, and get some light directly from the star and some reflected from the primary from the time it exits the umbra to the time it re-enters. Every day would have a full stellar eclipse at noon. Every night would see the primary cycle from waxing half through full to waning half. The space-facing side would have an ordinary day-night cycle with the same period as its orbital period around its primary.