When does a private fast (תענית יחיד) begin? At sunset or at dawn? Is it considered a fast like Yom Kippur (24 hr.) or like a half-day fast?
Are there any sources that address this?
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If an individual wants to take a fast upon himself, he must commit to do so the day before at mincha. [...] It makes no difference that he will continue to eat and drink after this until dawn.
On a private fast, one may rinse his mouth with water in the morning.
If one accepted upon himself to fast without any conditions, then he must do so until three stars come out at night
See also here.