If they’re tidally locked to each other, they’ll rotate once everytime they make a full rotation around each other. Eg if the planets orbit each other in 6 earth days and a point starts by facing the sun, three days later they’ll be facing away from the sun, and then another three days later they’ll be back to facing the sun. Their day/night cycle is 6 days.
What an interesting question! My first instinct is to say real world as mine is for a TTRPG, but when I actually start imagining it that doesn’t seem quite right. I guess it’s closer to a hyper realistic 3D render.