Yoma 1:8-2:1

Yoma 1:8

Every day of the year, a kohein took ashes from the altar around the time the rooster crowed but on Yom Kippur it was done at midnight (to give the Kohein Gadol time to rest before the morning service). On yom tov (when many sacrifices were offered), it was done after the first third of the night. On yom tov, the Temple courtyard would be full of Israelites bringing offerings even before the rooster crowed.

Yoma 2:1

Originally, whoever wanted to remove the ashes from the altar would just do so. If there were many people who desired to perform this task, they would run up the ramp and whoever reached the altar first got the job. In the event of a tie, they would draw lots by sticking out one or two fingers and counting. They wouldn’t stick out a thumb because this was not done in the Temple. (The Talmud says because it was a method of cheating.)