I'm having a debate about how bright Martian nights would be, in terms of both the sky itself and ground illumination. This answer seems to indicate that the stars would be only dimly visible, and wouldn't provide enough light to see by. However, the question remains of how much illumination the moons would provide. I've seen it said that Deimos would appear about as bright as Venus does from Earth, and that Phobos would be about twenty times brighter, but it's not clear to me how that compares to e.g. our own moon's illumination. So how bright would it look? Would it be enough to see by?
Taking Mars' average distance from the sun of 1.52 AU, the sun would be 43% as bright.
Phobos has an albedo of about 0.071 which is pretty dark. Darker than the Moon with an average albedo of about 0.12, so it reflects about 59% as well as the Moon does. That gives it a brightness to area of just over 25% the brightness of the moon.
Phobos is an odd shape, about 27x22x18 km. Averaging that out to 22, then Phobos is 1/158 the diameter of the Moon, but it's closer to Mars' surface. about 5,986 km, that's about 63.5 times closer than the Moon is to the surface of the Earth.
Working out the numbers, the size of phobos in the Martian sky would be on average 63.5/158 or 40% the diameter, or 16% the size of Earth's Moon from Earth. Multiply that by 25% the brightness to area and that's just 4% the brightness of a full moon. That would be peak brightness (and if you want to fuss about Mars' Perihelion and say 5% the brightness of a full moon, fair enough, but lets not get ahead of ourselves).
Brightness of our Moon varies depending how good a reflector it's surface is, and how much of the surface is in shadow. The Moon is particularly cratered so a half moon is significantly less than half as bright as a full moon. Phobos is so close to Mars that from the surface of Phobos, Mars takes up about 40 degrees of arc in the sky. That casts a huge shadow, so there's no such thing, from Mars, as a full Phobos. As Phobos approaches full, it enters Mars' shadow and it's brightness drops significantly (whether it turns red like a blood moon or just vanishes - I'm not sure, perhaps that's best for another question). But Phobos never becomes full, it gets a bit over 3/4s, then it enters Mars' shadow.
"Enough to see" is a tough question, because sight depends on not just the light source but the reflectivity of your surroundings and there's some variation in how well individuals can see in the dark and, obviously, on how clear the night sky is on Mars on that particular night. I think 3%-4% of the brightness of a 3/4 moon would be pushing the limit though and probably not bright enough to see for the most people. BUT reading the comments, and reading the very cool Venus shadow article in the questions comments, my assumption might be wrong. Limited sight might/(should?) be possible with some recognition of shadows and shapes.
Phobos's orbit is, like Mars' axis, inclined to Mars orbit by 25 degrees, so at greatest offset, I figure that Phobos is likely to be offset from the plane of Mars orbit by more than Mars' radius. Even at a periapsis distance of 9234km, 9234km*sine(25 degrees)=3902 km is more than Mars radius of 3390 km. So in winter and summer, there should be full Phobos.