[Answered myself below] I've seen similar questions have been asked before, but the details are slightly different.
Say you have a tidally-locked, roughly Earth-mass rocky planet in the habitable zone of an M-type red dwarf. That star is in a stable orbit with another star, a G-type star similar to our own sun (apologies, I don't know the orbital mechanics well enough to give exact distances and such here). Just to clarify, this is called an S-type planet, i.e. a planet in a binary star system which only orbits one of the stars. From what research I've done, this is a fairly common type of arrangement in our galaxy.
Obviously, the planet would have some kind of variation in illumination over time, but what kind of distances and luminosity would be required for it to have a "day/night" cycle broadly recognizable to humans (think within 18-36 hours)? Or would the cycle always take place moreso over the span of months/years in such an arrangement?