I am trying to grow basil (multiple varieties) on a south-facing
windowsill. I have no outdoor space to do this in, but in this
windowsill these plants will see the full sun for about 6 hours a day.
I can supplement the sun with some fluorescent lighting (mixed 'cool'
and 'warm' bulbs to about a third of the power (per area) of the sun).

I can not put every plant in the windowsill at once, nor can I put
every plant under the artificial light at once. Therefore, for optimum
light, I must rotate plants. This will result in unnatural periods of
light and darkness.

To what extent can basil tolerate unnatural periods of light and dark?
(Length of day vs night, variation of the length of one day to the
next, so on). Are scientific studies done on such topics? Will it vary
based on the particular variety?

Any insight into understanding how basil will respond to this sort of
situation would be much appreciated.