The pump for your DWC should be running 24/7 NOT tied in with the lights.
The reason for this is at least two fold-
1st. The plant roots need oxygen even in the dark, and the purpose of the pump is to keep to water super oxygenated to insure rapid and healthy root and plant growth and provide maximum nutrient uptake.
2nd. IF your pump is located outside of your box (easy enough to do) it can also help provide cool air that will help to keep the tank temperature low and help prevent root rot and algae.