"rest motionless" is a perfectly correct and usable phrase in written English.
You can use it when describing the physical movement of something or someone that is not moving, usually as a result of a command or situation. For example, "The soldier was commanded to rest motionless in the grass until the enemy had passed."
During the day, horn sharks rest motionless, hidden inside caves or crevices, or within thick mats of algae, though they remain relatively alert and will swim away quickly if disturbed.
A fixation cross against a black background was presented during the three 20-seconds long resting baseline epochs and subjects were instructed to not press any button and rest motionless as possible during these epochs.
In the small hours, down at the port, seagulls wheel around the cranes resting motionless, like giant, paralysed insects, against the illuminated pink clouds.
Susanne did not flinch and, after a few slow moments with his mouth resting motionless on hers, he inserted a pointed tongue.
It has also been seen resting motionless on the bottom.
Zebra sharks are nocturnal and spend most of the day resting motionless on the sea floor.
During the day, the sparsely-spotted stingaree spends much time resting motionless on the bottom, often buried in sand.
They have been documented resting motionless on the sea bottom or inside caves, unusual behavior for an active-swimming shark.
When garden warblers cross the Sahara, they fly at night, resting motionless and without feeding in suitable shade during the day.
During the day, the reticulate whipray is generally inactive and spends much time resting motionless on the sea floor, sometimes buried in sand.
During the day, Pacific angelsharks are almost never seen in the open, instead resting motionless on the sea floor buried under a thin layer of sediment that disguises their outlines.
