moonlit nights can be very good if you can find the bait and some current - especially in the spring.
in the fall, the outflow of creeks, jetties and out front in the surf can be outstanding when there's bait around - if the fish are there, you'll hear them before you see them.
a small rolling surf of 1-2 feet on a moonlit night is perfect for bass to lazily work the first wave and the backwash for bait, but the trick is find them when they are not schooled up yet.
being mobile is the key, take a long slow walk on the beach and listen and smell for everything as well as listen well. i'll sometimes walk two to three miles but stop and make a cast here and there occasionally, sometimes you just get a feeling.
sometimes its just one fish or two or three, but they could be 40" plus easy.
a good indicator can also be a small flock of gulls or terns sitting doing nothing. if they're out on a moonlit night rather than napping they know something - bait was or is nearby.
its one of my favourite times to fish - you don't need a headlamp (you shouldn't use one anyway) and very few people are out.