If I may comment again, I found a reference that questions the presumed location of the second temple:
The wikipedia entry also places the temple mount by the pool of Siloam:
“Second Temple period
During the Second Temple period, the King’s Garden was used as a staging area for Jewish pilgrims who, during the ]festivals of Passover, Shavuot and Sukkot, used the spring-fed Pool of Siloam to wash and ritually purify themselves before ascending the Great Staircase to the Temple Mount while singing hymns based on Psalms. On Sukkot water was brought from the Pool of Siloam to the Temple and poured upon the altar (Suk iv 9) and the priests also drank of this water (Ab. R. N. xxxv).”
The caution, always, is to “Call 811 before you dig”.