Seasonal lottery four months out, unclaimed spots released on the 15th at 10 a.m. MT, plus a daily lottery.
"An online Seasonal Lottery is held for all trips, all year, into the Left Fork of North Creek (Subway) to obtain a reservation for a Wilderness permit." Applications are "up to four months in advance", and "Unclaimed reservations become available to reserve on the 15th day of the month following the lottery, at 10am Mountain Time." A Daily Lottery takes applications "two days prior to a trip date, between 12:00 am MT and 3:00 pm MT", drawn at 3:00 pm MT. Confirmed on https://www.nps.gov/zion/planyourvisit/thesubway.htm. The 15th-of-the-month 10 a.m. release of unclaimed reservations and the daily lottery window are the scarcity moments this target watches for.
Updated , checked by hand against the target's own page.
Watched from nps.gov, the target's own public page — not a reservation system we poll.