My Pogonomyrmex Occidentalis are busy in on/off cycels without regard to day/night.
They just go into foraging mode every so often and the outworld is busy with many of them for about an hour or so at various times thoughout the day.
When not foraging as a focus they still have a few that keep watch in the outworld and may take up seed collection or whatever if i offer them something.
And the in nest activity is generally constant. movng the brood around, feeding brood, cracking seeds, helping new workers eclose, taking out trash, and so on.
As best a i can tell they are 24/7 ants that just flow back and forth between foraging mode and nest work mode every so often.
At least here in captivty anyway, and i have them under a light timer for a 14/10 hour day/night cycle.