Source for having a "Closing Prayer": Pesachim 54b
Not using one of the 24-blessing Prayers of fasts for rain: Pesachim 54b
Structure of the "Closing Prayer": Yoma 87b, Pesachim 3a
Including the Prayer admitting Sin in the "Closing Prayer": Yoma 87b, Pesachim 3a
The "Closing Prayer" Doubling as the Evening Prayer: Yoma 87b-88a, Pesachim 3a