The Red-eared Slider turtle refers to a semi-aquatic turtle that belongs to the family Emydidae. It is a native animal of the southern United States. They do sleep and their sleeping pattern is not determined or fixed. It depends on the habitat they live in.
Yes,RES do sleep when there is not much noise around them and when it is dark they often sleep when they are basking do you have a basking place for your turtles if not you should make a place in the wild they basking in the sun any where from 8 to 10 hours a day.
I have a female RES. She sleeps whenever she feels like it day or night... but she is easily awakened, usually just from the floor vibrations as I approach the area of her habitat. She's very trusting of humans as far as turtles go, so perhaps yours is just more sensitive to outside stimuli.