The success of making sun tea when the sun is absent hinges more critically on which factor?

The temperature the water reaches and how long it stays there

The fundamental principle behind sun tea is thermal energy transfer facilitating flavor extraction. When the direct solar radiation, which provides intense, focused heat, is removed due to cloud cover, the process essentially reverts to a passive warming scenario. Therefore, whether the brew succeeds or fails is determined by the actual energy absorbed by the water, which dictates the temperature achieved, and the duration for which that adequate temperature is maintained. Flavor compounds are extracted optimally only within a specific temperature window ($130^\circ\text{F}$ to $175^\circ\text{F}$), and if the water never reaches this level, regardless of how long it sits, the result will be weak or unsafe. The visual presence of the sun is secondary to the resulting thermal condition.